From 1f5cfd34b85e213892d61e0f3a277f4de41acffa Mon Sep 17 00:00:00 2001
From: agentmess <agentmess@users.noreply.github.com>
Date: Mon, 6 Jan 2025 18:59:38 +0000
Subject: [PATCH] deploy: 458704b8361b2435e4d00cdc03378794ea283e9a

---
 Accelerated Imaging Methods.html  |   2 +-
 Artifacts.html                    |   2 +-
 FOV and Resolution.html           |   2 +-
 Fast Imaging Pulse Sequences.html |   2 +-
 Fun with RF Pulses.html           |   2 +-
 Gradient and Spin Echoes.html     |   2 +-
 Image Reconstruction.html         |   6 +-
 Introduction.html                 |   2 +-
 K-space.html                      |  10 +-
 Key MRI Concepts.html             |   2 +-
 MR Physics - Bloch Equation.html  |   2 +-
 MRI Contrast.html                 |   2 +-
 MRI Math Concepts.html            |   2 +-
 MRI Notation.html                 |   2 +-
 MRI Signal Equation.html          |   2 +-
 MRI System.html                   |   2 +-
 Magnetic Fields and RF Coils.html |   2 +-
 Pulse Sequence.html               |   2 +-
 Questions.html                    |   2 +-
 RF Pulses.html                    |   2 +-
 Signal to Noise Ratio.html        |   2 +-
 Software_Resources.html           |   2 +-
 Spatial Encoding.html             | 278 +---------------
 Spectral-Spatial RF Pulses.html   |   2 +-
 Spin Physics.html                 |   2 +-
 _sources/K-space.ipynb            |   4 +-
 _sources/Spatial Encoding.ipynb   | 521 ------------------------------
 build_notes.html                  |   2 +-
 genindex.html                     |   2 +-
 objects.inv                       | Bin 798 -> 793 bytes
 reports/Spatial Encoding.err.log  |  59 ----
 search.html                       |   2 +-
 searchindex.js                    |   2 +-
 33 files changed, 39 insertions(+), 891 deletions(-)
 delete mode 100644 reports/Spatial Encoding.err.log

diff --git a/Accelerated Imaging Methods.html b/Accelerated Imaging Methods.html
index 34cbd41..e2bdd17 100644
--- a/Accelerated Imaging Methods.html	
+++ b/Accelerated Imaging Methods.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/Artifacts.html b/Artifacts.html
index 4aff67a..a005e42 100644
--- a/Artifacts.html
+++ b/Artifacts.html
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/FOV and Resolution.html b/FOV and Resolution.html
index a6fcc6a..f363ec8 100644
--- a/FOV and Resolution.html	
+++ b/FOV and Resolution.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/Fast Imaging Pulse Sequences.html b/Fast Imaging Pulse Sequences.html
index 6c301f0..52bcea4 100644
--- a/Fast Imaging Pulse Sequences.html	
+++ b/Fast Imaging Pulse Sequences.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/Fun with RF Pulses.html b/Fun with RF Pulses.html
index 1564a81..db3d430 100644
--- a/Fun with RF Pulses.html	
+++ b/Fun with RF Pulses.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/Gradient and Spin Echoes.html b/Gradient and Spin Echoes.html
index a69ce65..a81da04 100644
--- a/Gradient and Spin Echoes.html	
+++ b/Gradient and Spin Echoes.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/Image Reconstruction.html b/Image Reconstruction.html
index dd3b43d..222e5f6 100644
--- a/Image Reconstruction.html	
+++ b/Image Reconstruction.html	
@@ -75,7 +75,7 @@
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
     <link rel="next" title="Signal to Noise Ratio (SNR)" href="Signal%20to%20Noise%20Ratio.html" />
-    <link rel="prev" title="K-space Encoding" href="K-space.html" />
+    <link rel="prev" title="K-space" href="K-space.html" />
   <meta name="viewport" content="width=device-width, initial-scale=1"/>
   <meta name="docsearch:language" content="en"/>
   </head>
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="current nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
@@ -531,7 +531,7 @@ <h2>Fourier Transform Reconstruction<a class="headerlink" href="#fourier-transfo
       <i class="fa-solid fa-angle-left"></i>
       <div class="prev-next-info">
         <p class="prev-next-subtitle">previous</p>
-        <p class="prev-next-title">K-space Encoding</p>
+        <p class="prev-next-title">K-space</p>
       </div>
     </a>
     <a class="right-next"
diff --git a/Introduction.html b/Introduction.html
index f0cf387..aee07c0 100644
--- a/Introduction.html
+++ b/Introduction.html
@@ -190,7 +190,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/K-space.html b/K-space.html
index 29d9984..aa342dc 100644
--- a/K-space.html
+++ b/K-space.html
@@ -9,7 +9,7 @@
     <meta charset="utf-8" />
     <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
 
-    <title>K-space Encoding &#8212; Principles of MRI</title>
+    <title>K-space &#8212; Principles of MRI</title>
   
   
   
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="current nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1 current active"><a class="current reference internal" href="#">K-space Encoding</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
@@ -409,7 +409,7 @@
               
 
 <div id="jb-print-docs-body" class="onlyprint">
-    <h1>K-space Encoding</h1>
+    <h1>K-space</h1>
     <!-- Table of contents -->
     <div id="print-main-content">
         <div id="jb-print-toc">
@@ -441,8 +441,8 @@ <h2> Contents </h2>
 <div id="searchbox"></div>
                 <article class="bd-article" role="main">
                   
-  <section class="tex2jax_ignore mathjax_ignore" id="k-space-encoding">
-<h1>K-space Encoding<a class="headerlink" href="#k-space-encoding" title="Permalink to this heading">#</a></h1>
+  <section class="tex2jax_ignore mathjax_ignore" id="k-space">
+<h1>K-space<a class="headerlink" href="#k-space" title="Permalink to this heading">#</a></h1>
 <p>MRI is a so-called Fourier imaging technique, where data is acquired in the Fourier Transform domain.  The Fourier Transform domain is referred to as “k-space”.  This section describes the how to characterize MRI spatial encoding using k-space, including frequency encoding, phase encoding and other k-space trajectories.</p>
 <section id="learning-goals">
 <h2>Learning Goals<a class="headerlink" href="#learning-goals" title="Permalink to this heading">#</a></h2>
diff --git a/Key MRI Concepts.html b/Key MRI Concepts.html
index f9d729c..2f7ad9e 100644
--- a/Key MRI Concepts.html	
+++ b/Key MRI Concepts.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/MR Physics - Bloch Equation.html b/MR Physics - Bloch Equation.html
index ba2ec28..45941e0 100644
--- a/MR Physics - Bloch Equation.html	
+++ b/MR Physics - Bloch Equation.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/MRI Contrast.html b/MRI Contrast.html
index ad4bcbc..75b8f40 100644
--- a/MRI Contrast.html	
+++ b/MRI Contrast.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/MRI Math Concepts.html b/MRI Math Concepts.html
index 0bdab88..34f1085 100644
--- a/MRI Math Concepts.html	
+++ b/MRI Math Concepts.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/MRI Notation.html b/MRI Notation.html
index 7c324cb..39e80a4 100644
--- a/MRI Notation.html	
+++ b/MRI Notation.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/MRI Signal Equation.html b/MRI Signal Equation.html
index 3e956fd..ac18df2 100644
--- a/MRI Signal Equation.html	
+++ b/MRI Signal Equation.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/MRI System.html b/MRI System.html
index 44cf288..341c90e 100644
--- a/MRI System.html	
+++ b/MRI System.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/Magnetic Fields and RF Coils.html b/Magnetic Fields and RF Coils.html
index 068ed8f..d40c811 100644
--- a/Magnetic Fields and RF Coils.html	
+++ b/Magnetic Fields and RF Coils.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/Pulse Sequence.html b/Pulse Sequence.html
index 7513977..0bff353 100644
--- a/Pulse Sequence.html	
+++ b/Pulse Sequence.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/Questions.html b/Questions.html
index 79c33b8..bafb6ea 100644
--- a/Questions.html
+++ b/Questions.html
@@ -191,7 +191,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/RF Pulses.html b/RF Pulses.html
index 021e37a..22814dc 100644
--- a/RF Pulses.html	
+++ b/RF Pulses.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/Signal to Noise Ratio.html b/Signal to Noise Ratio.html
index 77e8800..6993b5d 100644
--- a/Signal to Noise Ratio.html	
+++ b/Signal to Noise Ratio.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/Software_Resources.html b/Software_Resources.html
index 1fd4482..00115e9 100644
--- a/Software_Resources.html
+++ b/Software_Resources.html
@@ -190,7 +190,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/Spatial Encoding.html b/Spatial Encoding.html
index 25e6aa6..fe0d26d 100644
--- a/Spatial Encoding.html	
+++ b/Spatial Encoding.html	
@@ -74,7 +74,7 @@
     <script>DOCUMENTATION_OPTIONS.pagename = 'Spatial Encoding';</script>
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
-    <link rel="next" title="K-space Encoding" href="K-space.html" />
+    <link rel="next" title="K-space" href="K-space.html" />
     <link rel="prev" title="MRI Contrast" href="MRI%20Contrast.html" />
   <meta name="viewport" content="width=device-width, initial-scale=1"/>
   <meta name="docsearch:language" content="en"/>
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="current nav bd-sidenav">
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
@@ -424,16 +424,6 @@ <h2> Contents </h2>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#k-space">k-space</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mri-signal">MRI signal</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#from-mri-data-to-images">From MRI data to images</a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#cartesian-k-space-frequency-and-phase-encoding-or-ft-imaging">Cartesian K-space (Frequency and Phase encoding, or FT Imaging)</a><ul class="nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#frequency-encoding">Frequency Encoding</a></li>
-</ul>
-</li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#phase-encoding">Phase Encoding</a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#frequency-and-phase-encoding">Frequency and Phase Encoding</a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#k-space-trajectories">K-space Trajectories</a><ul class="nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">K-space trajectories</a></li>
-</ul>
-</li>
 </ul>
             </nav>
         </div>
@@ -524,258 +514,6 @@ <h2>From MRI data to images<a class="headerlink" href="#from-mri-data-to-images"
 </ol>
 <p>We have now have the incredible result that we used magnetic field gradients, the k-space framework, and appropriate acquisition and ordering of the MR signal to create an <strong>IMAGE</strong>!!</p>
 </section>
-<section id="cartesian-k-space-frequency-and-phase-encoding-or-ft-imaging">
-<h2>Cartesian K-space (Frequency and Phase encoding, or FT Imaging)<a class="headerlink" href="#cartesian-k-space-frequency-and-phase-encoding-or-ft-imaging" title="Permalink to this heading">#</a></h2>
-<p>By far the most common way to perform spatial encoding is using a Cartesian k-space trajectory, which the name refers to the fact that data is sampled on a regularly spaced grid in k-space.
-This is also known FT imaging, since we reconstruct images with a 2D Fourier Transform.</p>
-<p>It consists of 2 types of encoding:</p>
-<ol class="arabic simple">
-<li><p>Frequency encoding - one dimension is encoded using a constant gradient applied during data acquisition</p></li>
-<li><p>Phase encoding - additional dimensions are encoded using gradient applied before data acquisition.  This gradient is incremented to provide complete spatial encoding.  Phase encoding is applied in 1 dimension for 2D imaging, and 2 dimensions for 3D imaging</p></li>
-</ol>
-<section id="frequency-encoding">
-<h3>Frequency Encoding<a class="headerlink" href="#frequency-encoding" title="Permalink to this heading">#</a></h3>
-<p>Typically 1 dimension of the object is encoded using “frequency encoding”.  This means that, after RF excitation, a magnetic field gradient is turned on and the signal is read out.  The frequencies present in the signal correspond to given spatial locations.  By convention, this is applied in the x-direction (but in practice can be rotated to any direction);</p>
-<div class="math notranslate nohighlight">
-\[f = \bar \gamma G_{xr} x\]</div>
-<p>where <span class="math notranslate nohighlight">\(G_{xr}\)</span> is the readout gradient amplitude.  Therefore, the position is proportional to the frequency:</p>
-<div class="math notranslate nohighlight">
-\[ x = \frac{f}{\bar \gamma G_{xr}}\]</div>
-<p>From frequency encoding data alone, a 1D image can be reconstructed with an inverse Fourier Transform</p>
-<div class="cell docutils container">
-<div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span> <span class="n">simulate</span> <span class="n">frequency</span> <span class="n">encoding</span>
-<span class="n">N</span> <span class="o">=</span> <span class="mi">8</span><span class="p">;</span>
-<span class="n">Mxy</span><span class="o">=</span> <span class="n">ones</span><span class="p">(</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">);</span>
-
-<span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">:</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">];</span>
-<span class="p">[</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">]</span> <span class="o">=</span> <span class="n">meshgrid</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">x</span><span class="p">);</span>
-<span class="n">Splot</span> <span class="o">=</span> <span class="mf">0.5</span><span class="p">;</span>
-
-<span class="n">kFE</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="mi">2</span><span class="p">;</span>
-<span class="n">dt</span> <span class="o">=</span> <span class="mf">0.1</span><span class="p">;</span>
-<span class="n">Tfe</span> <span class="o">=</span> <span class="mi">2</span><span class="p">;</span>
-
-<span class="n">GAMMA</span> <span class="o">=</span> <span class="mf">42.58</span><span class="p">;</span>
-
-
-<span class="k">for</span> <span class="n">tfe</span> <span class="o">=</span> <span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">6</span><span class="p">)</span><span class="o">*</span><span class="n">Tfe</span>
-    <span class="n">phase_x</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">kFE</span><span class="o">*</span><span class="n">x</span> <span class="o">*</span><span class="n">tfe</span><span class="o">/</span><span class="n">Tfe</span><span class="p">;</span>
-        
-    <span class="n">Mxy_FE</span> <span class="o">=</span> <span class="n">Mxy</span> <span class="o">.*</span> <span class="n">exp</span><span class="p">(</span><span class="n">i</span><span class="o">*</span><span class="n">phase_x</span><span class="p">);</span>
-        
-    <span class="n">figure</span>
-    <span class="n">subplot</span><span class="p">(</span><span class="mi">121</span><span class="p">),</span> <span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">:</span><span class="n">dt</span><span class="p">:</span><span class="n">Tfe</span><span class="o">+</span><span class="n">dt</span><span class="p">],</span>  <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">ones</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">Tfe</span><span class="o">/</span><span class="n">dt</span><span class="p">)</span><span class="o">*</span><span class="n">kFE</span><span class="o">/</span><span class="p">(</span><span class="n">Tfe</span><span class="o">/</span><span class="n">dt</span><span class="p">),</span> <span class="mi">0</span><span class="p">],</span> <span class="n">tfe</span><span class="o">*</span><span class="n">ones</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">),</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.05</span> <span class="mf">0.05</span><span class="p">]),</span> <span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;G_X&#39;</span><span class="p">)</span>
-    <span class="n">title</span><span class="p">(</span><span class="s1">&#39;Frequency Encoding&#39;</span><span class="p">)</span>
-    <span class="n">subplot</span><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
-    <span class="n">quiver</span><span class="p">(</span><span class="n">x</span><span class="o">-</span><span class="n">real</span><span class="p">(</span><span class="n">Mxy_FE</span><span class="p">)</span><span class="o">*</span><span class="n">Splot</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span><span class="n">y</span><span class="o">-</span><span class="n">imag</span><span class="p">(</span><span class="n">Mxy_FE</span><span class="p">)</span><span class="o">*</span><span class="n">Splot</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span><span class="n">real</span><span class="p">(</span><span class="n">Mxy_FE</span><span class="p">),</span> <span class="n">imag</span><span class="p">(</span><span class="n">Mxy_FE</span><span class="p">),</span> <span class="n">Splot</span><span class="p">)</span>
-    <span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;x&#39;</span><span class="p">),</span> <span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;y&#39;</span><span class="p">)</span>
-    <span class="n">xlim</span><span class="p">([</span><span class="o">-</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="o">+</span><span class="mi">1</span><span class="p">])</span>
-    <span class="n">ylim</span><span class="p">([</span><span class="o">-</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="o">+</span><span class="mi">1</span><span class="p">])</span>
-    <span class="n">title</span><span class="p">(</span><span class="s1">&#39;M_</span><span class="si">{XY}</span><span class="s1">&#39;</span><span class="p">)</span>
-    <span class="n">drawnow</span>
-<span class="n">end</span>
-</pre></div>
-</div>
-</div>
-<div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span>  <span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">5</span>
-    <span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">:</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">];</span>
-             <span class="o">^</span>
-<span class="ne">SyntaxError</span>: invalid syntax
-</pre></div>
-</div>
-</div>
-</div>
-</section>
-</section>
-<section id="phase-encoding">
-<h2>Phase Encoding<a class="headerlink" href="#phase-encoding" title="Permalink to this heading">#</a></h2>
-<p>Typically the 2nd (and optionally 3rd) dimensions of the object are encoded using “phase encoding”.  This means that, after RF excitation but before the frequency encoding gradient, a pulsed gradient is applied such that the location is encoded in the phase of the next magnetization:</p>
-<div class="math notranslate nohighlight">
-\[ \Phi(n) = \gamma (-G_{yp} + (n-1) G_{yi} ) t_y y\]</div>
-<p>This measurement is repeated for <span class="math notranslate nohighlight">\(n = 1, \ldots, N_{PE}\)</span>.  <span class="math notranslate nohighlight">\(G_{yp}\)</span> is the maximum phase encoding gradient strength, <span class="math notranslate nohighlight">\(G_{yi}\)</span> is the phase encoding gradient amplitude increment, and <span class="math notranslate nohighlight">\(t_y\)</span> is the phase encoding gradient duration.  Note that <span class="math notranslate nohighlight">\(2 G_{yp} = (N_{PE} - 1) G_{yi}\)</span>.</p>
-<p>These additional dimensions are fully encoded by repeating this pulsed gradient with different amplitudes.  This is equivalent to taking different samples of a frequency encoding gradient.</p>
-<div class="cell docutils container">
-<div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span> <span class="mi">2</span><span class="n">D</span> <span class="nb">object</span>
-<span class="o">%</span> <span class="n">simulate</span> <span class="n">frequencies</span> <span class="o">+</span> <span class="n">phase</span> <span class="n">encoding</span>
-
-<span class="n">N</span> <span class="o">=</span> <span class="mi">8</span><span class="p">;</span>
-<span class="n">Mxy</span><span class="o">=</span> <span class="n">ones</span><span class="p">(</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">);</span>
-
-<span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">:</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">];</span>
-<span class="p">[</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">]</span> <span class="o">=</span> <span class="n">meshgrid</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">x</span><span class="p">);</span>
-<span class="n">Splot</span> <span class="o">=</span> <span class="mf">0.5</span><span class="p">;</span>
-
-<span class="n">kPE</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">:</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">]</span><span class="o">/</span><span class="n">N</span><span class="p">;</span> <span class="o">%</span>
-<span class="n">dt</span> <span class="o">=</span> <span class="mf">0.1</span><span class="p">;</span>
-<span class="n">Tpe</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span>
-
-<span class="n">GAMMA</span> <span class="o">=</span> <span class="mf">42.58</span><span class="p">;</span>
-
-<span class="k">for</span> <span class="n">Ipe</span> <span class="o">=</span> <span class="mi">1</span><span class="p">:</span><span class="n">length</span><span class="p">(</span><span class="n">kPE</span><span class="p">)</span>
-    
-    <span class="k">for</span> <span class="n">tpe</span> <span class="o">=</span> <span class="n">Tpe</span> <span class="o">%</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">dt</span><span class="p">:</span><span class="n">Tpe</span><span class="p">]</span>
-        <span class="n">phase_y</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">kPE</span><span class="p">(</span><span class="n">Ipe</span><span class="p">)</span><span class="o">*</span><span class="n">y</span> <span class="o">*</span><span class="n">tpe</span><span class="o">/</span><span class="n">Tpe</span><span class="p">;</span>
-        
-        <span class="n">Mxy_PE</span> <span class="o">=</span> <span class="n">Mxy</span> <span class="o">.*</span> <span class="n">exp</span><span class="p">(</span><span class="n">i</span><span class="o">*</span><span class="n">phase_y</span><span class="p">);</span>
-        
-        <span class="n">figure</span><span class="p">(</span><span class="n">Ipe</span><span class="p">)</span>
-        
-        <span class="n">subplot</span><span class="p">(</span><span class="mi">121</span><span class="p">)</span>
-        <span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">:</span><span class="n">dt</span><span class="p">:</span><span class="n">Tpe</span><span class="o">+</span><span class="n">dt</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">ones</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">Tpe</span><span class="o">/</span><span class="n">dt</span><span class="p">)</span><span class="o">*</span><span class="n">kPE</span><span class="p">(</span><span class="n">Ipe</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">Tpe</span><span class="o">/</span><span class="n">dt</span><span class="p">),</span> <span class="mi">0</span><span class="p">]),</span> <span class="n">ylim</span><span class="p">([</span><span class="o">-</span><span class="mf">0.05</span> <span class="mf">0.05</span><span class="p">]),</span> <span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;G_Y&#39;</span><span class="p">)</span> 
-        <span class="n">title</span><span class="p">([</span><span class="s1">&#39;Phase encoding, Step &#39;</span> <span class="n">int2str</span><span class="p">(</span><span class="n">Ipe</span><span class="p">)])</span>
-        <span class="n">subplot</span><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
-        <span class="n">quiver</span><span class="p">(</span><span class="n">x</span><span class="o">-</span><span class="n">real</span><span class="p">(</span><span class="n">Mxy_PE</span><span class="p">)</span><span class="o">*</span><span class="n">Splot</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span><span class="n">y</span><span class="o">-</span><span class="n">imag</span><span class="p">(</span><span class="n">Mxy_PE</span><span class="p">)</span><span class="o">*</span><span class="n">Splot</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span><span class="n">real</span><span class="p">(</span><span class="n">Mxy_PE</span><span class="p">),</span> <span class="n">imag</span><span class="p">(</span><span class="n">Mxy_PE</span><span class="p">),</span> <span class="n">Splot</span><span class="p">)</span>
-        <span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;x&#39;</span><span class="p">),</span> <span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;y&#39;</span><span class="p">)</span>
-        <span class="n">xlim</span><span class="p">([</span><span class="o">-</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="o">+</span><span class="mi">1</span><span class="p">])</span>
-        <span class="n">ylim</span><span class="p">([</span><span class="o">-</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="o">+</span><span class="mi">1</span><span class="p">])</span>
-        <span class="n">title</span><span class="p">(</span><span class="s1">&#39;M_</span><span class="si">{XY}</span><span class="s1">&#39;</span><span class="p">)</span>
-        <span class="n">drawnow</span>
-    <span class="n">end</span>
-<span class="n">end</span>
-</pre></div>
-</div>
-</div>
-<div class="cell_output docutils container">
-<img alt="_images/e8157c8e2646b591cebc1497e61e0b35a6db60dc88f82732791c2e3cf6853c1d.png" src="_images/e8157c8e2646b591cebc1497e61e0b35a6db60dc88f82732791c2e3cf6853c1d.png" />
-<img alt="_images/a6fa61c88b8b5a66cb07c0e9435bcd54915f89f4461a50f15ae1ef8070edd4b7.png" src="_images/a6fa61c88b8b5a66cb07c0e9435bcd54915f89f4461a50f15ae1ef8070edd4b7.png" />
-<img alt="_images/93039522589251e0c593eac9deb6ffb011120e3750e4086dc8bc6655d6b2a42a.png" src="_images/93039522589251e0c593eac9deb6ffb011120e3750e4086dc8bc6655d6b2a42a.png" />
-<img alt="_images/d745bec0537600ab6a6e4855eb24aa73506635f0b90707164a822acb970662a7.png" src="_images/d745bec0537600ab6a6e4855eb24aa73506635f0b90707164a822acb970662a7.png" />
-<img alt="_images/1cdf78c961bf2f408eba613c20b43f09837510c1b2f1a10ea571aa5c4f9c0c91.png" src="_images/1cdf78c961bf2f408eba613c20b43f09837510c1b2f1a10ea571aa5c4f9c0c91.png" />
-<img alt="_images/02b013495b526e232f1e51521476aeee4346424df8c62a46d5a70f71412064c5.png" src="_images/02b013495b526e232f1e51521476aeee4346424df8c62a46d5a70f71412064c5.png" />
-<img alt="_images/b3698ba1e1d19e46c84a8e8477849ebf1c372adbf68de7584655cc1ac4f3a3b2.png" src="_images/b3698ba1e1d19e46c84a8e8477849ebf1c372adbf68de7584655cc1ac4f3a3b2.png" />
-<img alt="_images/6b498db82f8fd884a4ee33ce2be5e3f46d68600f324d095ee38180f4610835f8.png" src="_images/6b498db82f8fd884a4ee33ce2be5e3f46d68600f324d095ee38180f4610835f8.png" />
-<img alt="_images/b2ebaf1ffc7beaa5180e2c06110c556ecdf7ae48c942e0bb7f7822ff236d55b1.png" src="_images/b2ebaf1ffc7beaa5180e2c06110c556ecdf7ae48c942e0bb7f7822ff236d55b1.png" />
-</div>
-</div>
-</section>
-<section id="frequency-and-phase-encoding">
-<h2>Frequency and Phase Encoding<a class="headerlink" href="#frequency-and-phase-encoding" title="Permalink to this heading">#</a></h2>
-<p>The following simulation of the net magnetizations shows how first the phase encoding gradient (<span class="math notranslate nohighlight">\(G_Y\)</span>) creates some phase variation in <span class="math notranslate nohighlight">\(y\)</span>, and then during the frequency encoding gradient (<span class="math notranslate nohighlight">\(G_X\)</span>) the net magnetizations rotate at varying frequencies depending on their <span class="math notranslate nohighlight">\(x\)</span> position:</p>
-<p><img alt="frequency_phase_encoding-simple-Mxy.gif" src="_images/frequency_phase_encoding-simple-Mxy.gif" /></p>
-<p>Instead of viewing the net magnetizations, we can also visualize this encoding as a map of the phase of the transverse magnetization:</p>
-<p><img alt="frequency_phase_encoding-simple-image_phase.gif" src="_images/frequency_phase_encoding-simple-image_phase.gif" /></p>
-<p>(See <code class="docutils literal notranslate"><span class="pre">spatial_encoding_Mxy_illustration.m</span></code> for code generating this movie)</p>
-</section>
-<section id="k-space-trajectories">
-<h2>K-space Trajectories<a class="headerlink" href="#k-space-trajectories" title="Permalink to this heading">#</a></h2>
-<p>K-space is a very general method for capturing the effect of spatial encoding gradients, and the “k-space trajectory” is defined as the pattern created over time by the gradients:</p>
-<div class="math notranslate nohighlight">
-\[\vec{k}(t) = \frac{\gamma}{2\pi} \int_0^t \vec{G}(\tau) d\tau\]</div>
-<p>Note that k-space trajectories always start at the center of k-space, <span class="math notranslate nohighlight">\(\vec{k}(0) = 0\)</span> and are only defined once there is transverse magnetization (e.g. after an RF pulse).</p>
-<p>The following simulation of the net magnetizations shows how rotations and k-space trajectory during a typical Cartesian (or 2D FT) gradient pulse sequence, which is differs from the simulation above in that an initial dephasing gradient in the frequency encoding direction is applied to sample both positive and negative spatial frequencies in k-space:</p>
-<p><img alt="frequency_phase_encoding-full-Mxy.gif" src="_images/frequency_phase_encoding-full-Mxy.gif" /></p>
-<p><img alt="frequency_phase_encoding-full-image_phase.gif" src="_images/frequency_phase_encoding-full-image_phase.gif" /></p>
-<p>(See <code class="docutils literal notranslate"><span class="pre">spatial_encoding_Mxy_illustration.m</span></code> for code generating this movie)</p>
-<section id="id1">
-<h3>K-space trajectories<a class="headerlink" href="#id1" title="Permalink to this heading">#</a></h3>
-<p>The k-space pattern during a MRI experiment is referred to as the k-space “trajectory”.  The most common are Cartesian trajectories, in which parallel lines of k-space are covered to sample a 2D (or 3D) grid.  K-space trajectories with other patterns, such as radial lines, spirals, rastered lines (echo-planar trajectories), or blades can also be used.</p>
-<div class="cell docutils container">
-<div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span>  <span class="n">plot</span> <span class="mi">2</span><span class="n">D</span> <span class="n">k</span><span class="o">-</span><span class="n">space</span> <span class="n">trajectories</span>
-
-<span class="o">%</span> <span class="n">Cartesian</span>
-<span class="n">N</span> <span class="o">=</span> <span class="mi">8</span><span class="p">;</span>
-
-<span class="n">k</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">:</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">]</span><span class="o">/</span><span class="n">N</span><span class="p">;</span>
-<span class="p">[</span><span class="n">ky</span><span class="p">,</span><span class="n">kx</span><span class="p">]</span> <span class="o">=</span> <span class="n">meshgrid</span><span class="p">(</span><span class="n">k</span><span class="p">,</span><span class="n">k</span><span class="p">);</span>
-
-<span class="n">figure</span>
-<span class="n">plot</span><span class="p">(</span><span class="n">kx</span><span class="p">,</span> <span class="n">ky</span><span class="p">,</span> <span class="s1">&#39;LineWidth&#39;</span><span class="p">,</span><span class="mi">10</span><span class="p">),</span> <span class="n">xlim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">]),</span> <span class="n">ylim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">])</span>
-<span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;k_x&#39;</span><span class="p">),</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;k_y&#39;</span><span class="p">)</span>
-<span class="n">title</span><span class="p">(</span><span class="s1">&#39;Cartesian trajectory&#39;</span><span class="p">)</span>
-
-<span class="o">%</span> <span class="n">echo</span><span class="o">-</span><span class="n">planar</span>
-<span class="n">kx_ep</span> <span class="o">=</span> <span class="n">kx</span><span class="p">;</span> <span class="n">kx_ep</span><span class="p">(:,</span><span class="mi">2</span><span class="p">:</span><span class="mi">2</span><span class="p">:</span><span class="n">end</span><span class="p">)</span> <span class="o">=</span> <span class="n">kx_ep</span><span class="p">(</span><span class="n">end</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">:</span><span class="mi">2</span><span class="p">:</span><span class="n">end</span><span class="p">);</span>
-<span class="n">kx_ep</span> <span class="o">=</span> <span class="n">kx_ep</span><span class="p">(:);</span>
-
-<span class="n">ky_ep</span> <span class="o">=</span> <span class="n">ky</span><span class="p">(:);</span>
-
-<span class="n">figure</span>
-<span class="n">plot</span><span class="p">(</span><span class="n">kx_ep</span><span class="p">,</span> <span class="n">ky_ep</span><span class="p">,</span> <span class="s1">&#39;LineWidth&#39;</span><span class="p">,</span><span class="mi">10</span><span class="p">),</span> <span class="n">xlim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">]),</span> <span class="n">ylim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">])</span>
-<span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;k_x&#39;</span><span class="p">),</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;k_y&#39;</span><span class="p">)</span>
-<span class="n">title</span><span class="p">(</span><span class="s1">&#39;Echo-Planar trajectory&#39;</span><span class="p">)</span>
-
-<span class="o">%</span> <span class="n">radial</span>
-
-<span class="n">k_theta</span> <span class="o">=</span> <span class="n">exp</span><span class="p">(</span><span class="n">i</span><span class="o">*</span><span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="n">N</span><span class="p">]</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">N</span><span class="p">));</span>
-<span class="n">k_radial</span> <span class="o">=</span> <span class="n">k</span><span class="o">.</span><span class="s1">&#39; * k_theta;</span>
-
-<span class="n">figure</span>
-<span class="n">plot</span><span class="p">(</span><span class="n">real</span><span class="p">(</span><span class="n">k_radial</span><span class="p">),</span> <span class="n">imag</span><span class="p">(</span><span class="n">k_radial</span><span class="p">),</span> <span class="s1">&#39;LineWidth&#39;</span><span class="p">,</span><span class="mi">10</span><span class="p">),</span> <span class="n">xlim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">]),</span> <span class="n">ylim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">])</span>
-<span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;k_x&#39;</span><span class="p">),</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;k_y&#39;</span><span class="p">)</span>
-<span class="n">title</span><span class="p">(</span><span class="s1">&#39;Radial trajectory&#39;</span><span class="p">)</span>
-
-
-<span class="o">%</span> <span class="n">spiral</span>
-<span class="n">n</span> <span class="o">=</span> <span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">201</span><span class="p">);</span>
-<span class="n">Nturns</span> <span class="o">=</span> <span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">;</span>
-<span class="n">k_spiral</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="mi">2</span><span class="o">*</span><span class="n">n</span><span class="o">.*</span><span class="n">exp</span><span class="p">(</span><span class="n">i</span><span class="o">*</span><span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">Nturns</span><span class="o">*</span><span class="n">n</span><span class="p">);</span>
-
-<span class="n">figure</span>
-<span class="n">plot</span><span class="p">(</span><span class="n">real</span><span class="p">(</span><span class="n">k_spiral</span><span class="p">),</span> <span class="n">imag</span><span class="p">(</span><span class="n">k_spiral</span><span class="p">),</span> <span class="s1">&#39;LineWidth&#39;</span><span class="p">,</span><span class="mi">10</span><span class="p">),</span> <span class="n">xlim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">]),</span> <span class="n">ylim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">])</span>
-<span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;k_x&#39;</span><span class="p">),</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;k_y&#39;</span><span class="p">)</span>
-<span class="n">title</span><span class="p">(</span><span class="s1">&#39;Spiral trajectory&#39;</span><span class="p">)</span>
-</pre></div>
-</div>
-</div>
-<div class="cell_output docutils container">
-<img alt="_images/5b39e1ebc881f649c67f5ac15ce8c8a75e4a4c90e457944d4fcdebecb9765e0e.png" src="_images/5b39e1ebc881f649c67f5ac15ce8c8a75e4a4c90e457944d4fcdebecb9765e0e.png" />
-<img alt="_images/7fb4dad9c315d2e6180b1051ed906c6aa4d468982a0a6b51fb2c3ce32f3b84b0.png" src="_images/7fb4dad9c315d2e6180b1051ed906c6aa4d468982a0a6b51fb2c3ce32f3b84b0.png" />
-<img alt="_images/682a80458c6d6462569bebe71790fb3febb4b4c02786b73b1137a08da5e5bd7d.png" src="_images/682a80458c6d6462569bebe71790fb3febb4b4c02786b73b1137a08da5e5bd7d.png" />
-<img alt="_images/2149bec492121a4c0c21ee11bde6587912c06f6bb9a9c159cbccaa6653da593c.png" src="_images/2149bec492121a4c0c21ee11bde6587912c06f6bb9a9c159cbccaa6653da593c.png" />
-</div>
-</div>
-<div class="cell docutils container">
-<div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span>  <span class="n">plot</span> <span class="mi">3</span><span class="n">D</span> <span class="n">k</span><span class="o">-</span><span class="n">space</span> <span class="n">trajectories</span>
-
-<span class="o">%</span> <span class="n">Cartesian</span>
-<span class="n">N</span> <span class="o">=</span> <span class="mi">8</span><span class="p">;</span>
-
-<span class="n">k</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">:</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">]</span><span class="o">/</span><span class="n">N</span><span class="p">;</span>
-<span class="p">[</span><span class="n">ky</span><span class="p">,</span><span class="n">kx</span><span class="p">,</span><span class="n">kz</span><span class="p">]</span> <span class="o">=</span> <span class="n">meshgrid</span><span class="p">(</span><span class="n">k</span><span class="p">,</span><span class="n">k</span><span class="p">,</span><span class="n">k</span><span class="p">);</span>
-
-
-<span class="n">figure</span>
-<span class="n">plot3</span><span class="p">(</span><span class="n">reshape</span><span class="p">(</span><span class="n">kx</span><span class="p">,</span> <span class="p">[</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span> <span class="p">(</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">^</span><span class="mi">2</span><span class="p">]),</span> <span class="n">reshape</span><span class="p">(</span><span class="n">ky</span><span class="p">,</span> <span class="p">[</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span> <span class="p">(</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">^</span><span class="mi">2</span><span class="p">]),</span> <span class="n">reshape</span><span class="p">(</span><span class="n">kz</span><span class="p">,</span> <span class="p">[</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span> <span class="p">(</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">^</span><span class="mi">2</span><span class="p">]),</span> <span class="s1">&#39;LineWidth&#39;</span><span class="p">,</span><span class="mi">10</span><span class="p">)</span>
-<span class="n">xlim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">]),</span> <span class="n">ylim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">]),</span> <span class="n">zlim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">])</span>
-<span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;k_x&#39;</span><span class="p">),</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;k_y&#39;</span><span class="p">),</span> <span class="n">zlabel</span><span class="p">(</span><span class="s1">&#39;k_z&#39;</span><span class="p">)</span>
-<span class="n">title</span><span class="p">(</span><span class="s1">&#39;Cartesian trajectory&#39;</span><span class="p">)</span>
-
-<span class="o">%</span> <span class="n">radial</span>
-
-<span class="n">N_radial</span> <span class="o">=</span> <span class="n">N</span><span class="o">^</span><span class="mi">3</span><span class="p">;</span>
-
-<span class="n">n</span> <span class="o">=</span> <span class="mi">1</span><span class="p">:</span><span class="n">N_radial</span><span class="p">;</span>
-
-<span class="n">kz</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">n</span> <span class="o">-</span> <span class="n">N_radial</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">N_radial</span><span class="p">;</span>
-<span class="n">kx</span> <span class="o">=</span> <span class="n">cos</span><span class="p">(</span><span class="n">sqrt</span><span class="p">(</span><span class="n">N_radial</span><span class="o">*</span><span class="n">pi</span><span class="p">)</span> <span class="o">.*</span> <span class="n">asin</span><span class="p">(</span><span class="n">kz</span><span class="p">))</span> <span class="o">.*</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">kz</span><span class="o">.^</span><span class="mi">2</span><span class="p">);</span>
-<span class="n">ky</span> <span class="o">=</span> <span class="n">sin</span><span class="p">(</span><span class="n">sqrt</span><span class="p">(</span><span class="n">N_radial</span><span class="o">*</span><span class="n">pi</span><span class="p">)</span> <span class="o">.*</span> <span class="n">asin</span><span class="p">(</span><span class="n">kz</span><span class="p">))</span> <span class="o">.*</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">kz</span><span class="o">.^</span><span class="mi">2</span><span class="p">);</span>
-
-<span class="n">figure</span>
-<span class="n">plot3</span><span class="p">([</span><span class="n">zeros</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">N_radial</span><span class="p">);</span> <span class="n">kx</span><span class="p">],</span> <span class="p">[</span><span class="n">zeros</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">N_radial</span><span class="p">);</span> <span class="n">ky</span><span class="p">],</span> <span class="p">[</span><span class="n">zeros</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">N_radial</span><span class="p">);</span> <span class="n">kz</span><span class="p">])</span>
-<span class="n">xlim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">]),</span> <span class="n">ylim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">]),</span> <span class="n">zlim</span><span class="p">([</span><span class="o">-</span><span class="mf">.6</span> <span class="mf">.6</span><span class="p">])</span>
-<span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;k_x&#39;</span><span class="p">),</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;k_y&#39;</span><span class="p">),</span> <span class="n">zlabel</span><span class="p">(</span><span class="s1">&#39;k_z&#39;</span><span class="p">)</span>
-<span class="n">title</span><span class="p">(</span><span class="s1">&#39;Radial trajectory&#39;</span><span class="p">)</span>
-</pre></div>
-</div>
-</div>
-<div class="cell_output docutils container">
-<img alt="_images/5b39e1ebc881f649c67f5ac15ce8c8a75e4a4c90e457944d4fcdebecb9765e0e.png" src="_images/5b39e1ebc881f649c67f5ac15ce8c8a75e4a4c90e457944d4fcdebecb9765e0e.png" />
-<img alt="_images/7fb4dad9c315d2e6180b1051ed906c6aa4d468982a0a6b51fb2c3ce32f3b84b0.png" src="_images/7fb4dad9c315d2e6180b1051ed906c6aa4d468982a0a6b51fb2c3ce32f3b84b0.png" />
-<img alt="_images/682a80458c6d6462569bebe71790fb3febb4b4c02786b73b1137a08da5e5bd7d.png" src="_images/682a80458c6d6462569bebe71790fb3febb4b4c02786b73b1137a08da5e5bd7d.png" />
-<img alt="_images/2149bec492121a4c0c21ee11bde6587912c06f6bb9a9c159cbccaa6653da593c.png" src="_images/2149bec492121a4c0c21ee11bde6587912c06f6bb9a9c159cbccaa6653da593c.png" />
-</div>
-</div>
-<p>These movies illustrate the phase accumulation during non-Cartesian trajectories</p>
-<p><img alt="radial_encoding-full-Mxy.gif" src="_images/radial_encoding-full-Mxy.gif" /></p>
-<p><img alt="spiral_encoding-full-Mxy.gif" src="_images/spiral_encoding-full-Mxy.gif" /></p>
-<p>(See <code class="docutils literal notranslate"><span class="pre">spatial_encoding_Mxy_illustration.m</span></code> for code generating this movie)</p>
-</section>
-</section>
 </section>
 
     <script type="text/x-thebe-config">
@@ -822,7 +560,7 @@ <h3>K-space trajectories<a class="headerlink" href="#id1" title="Permalink to th
        title="next page">
       <div class="prev-next-info">
         <p class="prev-next-subtitle">next</p>
-        <p class="prev-next-title">K-space Encoding</p>
+        <p class="prev-next-title">K-space</p>
       </div>
       <i class="fa-solid fa-angle-right"></i>
     </a>
@@ -846,16 +584,6 @@ <h3>K-space trajectories<a class="headerlink" href="#id1" title="Permalink to th
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#k-space">k-space</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mri-signal">MRI signal</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#from-mri-data-to-images">From MRI data to images</a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#cartesian-k-space-frequency-and-phase-encoding-or-ft-imaging">Cartesian K-space (Frequency and Phase encoding, or FT Imaging)</a><ul class="nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#frequency-encoding">Frequency Encoding</a></li>
-</ul>
-</li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#phase-encoding">Phase Encoding</a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#frequency-and-phase-encoding">Frequency and Phase Encoding</a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#k-space-trajectories">K-space Trajectories</a><ul class="nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">K-space trajectories</a></li>
-</ul>
-</li>
 </ul>
   </nav></div>
 
diff --git a/Spectral-Spatial RF Pulses.html b/Spectral-Spatial RF Pulses.html
index 026a370..b3caa1b 100644
--- a/Spectral-Spatial RF Pulses.html	
+++ b/Spectral-Spatial RF Pulses.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/Spin Physics.html b/Spin Physics.html
index 067da1c..85ab776 100644
--- a/Spin Physics.html	
+++ b/Spin Physics.html	
@@ -193,7 +193,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/_sources/K-space.ipynb b/_sources/K-space.ipynb
index 37d71a0..b13b6a0 100644
--- a/_sources/K-space.ipynb
+++ b/_sources/K-space.ipynb
@@ -4,7 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# K-space Encoding\n",
+    "# K-space\n",
     "\n",
     "MRI is a so-called Fourier imaging technique, where data is acquired in the Fourier Transform domain.  The Fourier Transform domain is referred to as \"k-space\".  This section describes the how to characterize MRI spatial encoding using k-space, including frequency encoding, phase encoding and other k-space trajectories.\n",
     "\n",
@@ -43,7 +43,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "metadata": {},
    "outputs": [
     {
diff --git a/_sources/Spatial Encoding.ipynb b/_sources/Spatial Encoding.ipynb
index dd9384b..79d6ca3 100644
--- a/_sources/Spatial Encoding.ipynb	
+++ b/_sources/Spatial Encoding.ipynb	
@@ -100,527 +100,6 @@
     "\n",
     "We have now have the incredible result that we used magnetic field gradients, the k-space framework, and appropriate acquisition and ordering of the MR signal to create an **IMAGE**!!"
    ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Cartesian K-space (Frequency and Phase encoding, or FT Imaging)\n",
-    "\n",
-    "By far the most common way to perform spatial encoding is using a Cartesian k-space trajectory, which the name refers to the fact that data is sampled on a regularly spaced grid in k-space.\n",
-    "This is also known FT imaging, since we reconstruct images with a 2D Fourier Transform.\n",
-    "\n",
-    "It consists of 2 types of encoding:\n",
-    "1. Frequency encoding - one dimension is encoded using a constant gradient applied during data acquisition\n",
-    "1. Phase encoding - additional dimensions are encoded using gradient applied before data acquisition.  This gradient is incremented to provide complete spatial encoding.  Phase encoding is applied in 1 dimension for 2D imaging, and 2 dimensions for 3D imaging\n",
-    "\n",
-    "### Frequency Encoding\n",
-    "\n",
-    "Typically 1 dimension of the object is encoded using \"frequency encoding\".  This means that, after RF excitation, a magnetic field gradient is turned on and the signal is read out.  The frequencies present in the signal correspond to given spatial locations.  By convention, this is applied in the x-direction (but in practice can be rotated to any direction);\n",
-    "\n",
-    "$$f = \\bar \\gamma G_{xr} x$$\n",
-    "where $G_{xr}$ is the readout gradient amplitude.  Therefore, the position is proportional to the frequency:\n",
-    "\n",
-    "$$ x = \\frac{f}{\\bar \\gamma G_{xr}}$$\n",
-    "\n",
-    "From frequency encoding data alone, a 1D image can be reconstructed with an inverse Fourier Transform"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "% simulate frequency encoding\n",
-    "N = 8;\n",
-    "Mxy= ones(N+1,N+1);\n",
-    "\n",
-    "x = [-N/2:N/2];\n",
-    "[x,y] = meshgrid(x,x);\n",
-    "Splot = 0.5;\n",
-    "\n",
-    "kFE = 1/2;\n",
-    "dt = 0.1;\n",
-    "Tfe = 2;\n",
-    "\n",
-    "GAMMA = 42.58;\n",
-    "\n",
-    "\n",
-    "for tfe = linspace(0,1,6)*Tfe\n",
-    "    phase_x = 2*pi*kFE*x *tfe/Tfe;\n",
-    "        \n",
-    "    Mxy_FE = Mxy .* exp(i*phase_x);\n",
-    "        \n",
-    "    figure\n",
-    "    subplot(121), plot([0:dt:Tfe+dt],  [0, ones(1,Tfe/dt)*kFE/(Tfe/dt), 0], tfe*ones(1,2), [-0.05 0.05]), ylabel('G_X')\n",
-    "    title('Frequency Encoding')\n",
-    "    subplot(122)\n",
-    "    quiver(x-real(Mxy_FE)*Splot/2,y-imag(Mxy_FE)*Splot/2,real(Mxy_FE), imag(Mxy_FE), Splot)\n",
-    "    xlabel('x'), ylabel('y')\n",
-    "    xlim([-N/2-1, N/2+1])\n",
-    "    ylim([-N/2-1, N/2+1])\n",
-    "    title('M_{XY}')\n",
-    "    drawnow\n",
-    "end\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Phase Encoding\n",
-    "\n",
-    "Typically the 2nd (and optionally 3rd) dimensions of the object are encoded using \"phase encoding\".  This means that, after RF excitation but before the frequency encoding gradient, a pulsed gradient is applied such that the location is encoded in the phase of the next magnetization:\n",
-    "\n",
-    "$$ \\Phi(n) = \\gamma (-G_{yp} + (n-1) G_{yi} ) t_y y$$ \n",
-    "\n",
-    "This measurement is repeated for $n = 1, \\ldots, N_{PE}$.  $G_{yp}$ is the maximum phase encoding gradient strength, $G_{yi}$ is the phase encoding gradient amplitude increment, and $t_y$ is the phase encoding gradient duration.  Note that $2 G_{yp} = (N_{PE} - 1) G_{yi}$.\n",
-    "\n",
-    "These additional dimensions are fully encoded by repeating this pulsed gradient with different amplitudes.  This is equivalent to taking different samples of a frequency encoding gradient."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjAAAAGkCAIAAACgjIjwAAAJMmlDQ1BkZWZhdWx0X3JnYi5pY2MAAEiJlZVnUJNZF8fv8zzphUASQodQQ5EqJYCUEFoo0quoQOidUEVsiLgCK4qINEWQRQEXXJUia0UUC4uCAhZ0gywCyrpxFVFBWXDfGZ33HT+8/5l7z2/+c+bec8/5cAEgiINlwct7YlK6wNvJjhkYFMwE3yiMn5bC8fR0A9/VuxEArcR7ut/P+a4IEZFp/OW4uLxy+SmCdACg7GXWzEpPWeGjy0wPj//CZ1dYsFzgMt9Y4eh/eexLzr8s+pLj681dfhUKABwp+hsO/4b/c++KVDiC9NioyGymT3JUelaYIJKZttIJHpfL9BQkR8UmRH5T8P+V/B2lR2anr0RucsomQWx0TDrzfw41MjA0BF9n8cbrS48hRv9/z2dFX73kegDYcwAg+7564ZUAdO4CQPrRV09tua+UfAA67vAzBJn/eqiVDQ0IgALoQAYoAlWgCXSBETADlsAWOAAX4AF8QRDYAPggBiQCAcgCuWAHKABFYB84CKpALWgATaAVnAad4Dy4Aq6D2+AuGAaPgRBMgpdABN6BBQiCsBAZokEykBKkDulARhAbsoYcIDfIGwqCQqFoKAnKgHKhnVARVApVQXVQE/QLdA66At2EBqGH0Dg0A/0NfYQRmATTYQVYA9aH2TAHdoV94fVwNJwK58D58F64Aq6HT8Id8BX4NjwMC+GX8BwCECLCQJQRXYSNcBEPJBiJQgTIVqQQKUfqkVakG+lD7iFCZBb5gMKgaCgmShdliXJG+aH4qFTUVlQxqgp1AtWB6kXdQ42jRKjPaDJaHq2DtkDz0IHoaHQWugBdjm5Et6OvoYfRk+h3GAyGgWFhzDDOmCBMHGYzphhzGNOGuYwZxExg5rBYrAxWB2uF9cCGYdOxBdhK7EnsJewQdhL7HkfEKeGMcI64YFwSLg9XjmvGXcQN4aZwC3hxvDreAu+Bj8BvwpfgG/Dd+Dv4SfwCQYLAIlgRfAlxhB2ECkIr4RphjPCGSCSqEM2JXsRY4nZiBfEU8QZxnPiBRCVpk7ikEFIGaS/pOOky6SHpDZlM1iDbkoPJ6eS95CbyVfJT8nsxmpieGE8sQmybWLVYh9iQ2CsKnqJO4VA2UHIo5ZQzlDuUWXG8uIY4VzxMfKt4tfg58VHxOQmahKGEh0SiRLFEs8RNiWkqlqpBdaBGUPOpx6hXqRM0hKZK49L4tJ20Bto12iQdQ2fRefQ4ehH9Z/oAXSRJlTSW9JfMlqyWvCApZCAMDQaPkcAoYZxmjDA+SilIcaQipfZItUoNSc1Ly0nbSkdKF0q3SQ9Lf5RhyjjIxMvsl+mUeSKLktWW9ZLNkj0ie012Vo4uZynHlyuUOy33SB6W15b3lt8sf0y+X35OQVHBSSFFoVLhqsKsIkPRVjFOsUzxouKMEk3JWilWqUzpktILpiSTw0xgVjB7mSJleWVn5QzlOuUB5QUVloqfSp5Km8oTVYIqWzVKtUy1R1WkpqTmrpar1qL2SB2vzlaPUT+k3qc+r8HSCNDYrdGpMc2SZvFYOawW1pgmWdNGM1WzXvO+FkaLrRWvdVjrrjasbaIdo12tfUcH1jHVidU5rDO4Cr3KfFXSqvpVo7okXY5upm6L7rgeQ89NL0+vU++Vvpp+sP5+/T79zwYmBgkGDQaPDamGLoZ5ht2GfxtpG/GNqo3uryavdly9bXXX6tfGOsaRxkeMH5jQTNxNdpv0mHwyNTMVmLaazpipmYWa1ZiNsulsT3Yx+4Y52tzOfJv5efMPFqYW6RanLf6y1LWMt2y2nF7DWhO5pmHNhJWKVZhVnZXQmmkdan3UWmijbBNmU2/zzFbVNsK20XaKo8WJ45zkvLIzsBPYtdvNcy24W7iX7RF7J/tC+wEHqoOfQ5XDU0cVx2jHFkeRk4nTZqfLzmhnV+f9zqM8BR6f18QTuZi5bHHpdSW5+rhWuT5z03YTuHW7w+4u7gfcx9aqr01a2+kBPHgeBzyeeLI8Uz1/9cJ4eXpVez33NvTO9e7zofls9Gn2eedr51vi+9hP0y/Dr8ef4h/i3+Q/H2AfUBogDNQP3BJ4O0g2KDaoKxgb7B/cGDy3zmHdwXWTISYhBSEj61nrs9ff3CC7IWHDhY2UjWEbz4SiQwNCm0MXwzzC6sPmwnnhNeEiPpd/iP8ywjaiLGIm0iqyNHIqyiqqNGo62ir6QPRMjE1MecxsLDe2KvZ1nHNcbdx8vEf88filhICEtkRcYmjiuSRqUnxSb7JicnbyYIpOSkGKMNUi9WCqSOAqaEyD0tandaXTlz/F/gzNjF0Z45nWmdWZ77P8s85kS2QnZfdv0t60Z9NUjmPOT5tRm/mbe3KVc3fkjm/hbKnbCm0N39qzTXVb/rbJ7U7bT+wg7Ijf8VueQV5p3tudATu78xXyt+dP7HLa1VIgViAoGN1tubv2B9QPsT8M7Fm9p3LP58KIwltFBkXlRYvF/OJbPxr+WPHj0t6ovQMlpiVH9mH2Je0b2W+z/0SpRGlO6cQB9wMdZcyywrK3BzcevFluXF57iHAo45Cwwq2iq1Ktcl/lYlVM1XC1XXVbjXzNnpr5wxGHh47YHmmtVagtqv14NPbogzqnuo56jfryY5hjmceeN/g39P3E/qmpUbaxqPHT8aTjwhPeJ3qbzJqamuWbS1rgloyWmZMhJ+/+bP9zV6tua10bo63oFDiVcerFL6G/jJx2Pd1zhn2m9az62Zp2WnthB9SxqUPUGdMp7ArqGjzncq6n27K7/Ve9X4+fVz5ffUHyQslFwsX8i0uXci7NXU65PHsl+spEz8aex1cDr97v9eoduOZ67cZ1x+tX+zh9l25Y3Th/0+LmuVvsW523TW939Jv0t/9m8lv7gOlAxx2zO113ze92D64ZvDhkM3Tlnv296/d5928Prx0eHPEbeTAaMip8EPFg+mHCw9ePMh8tPN4+hh4rfCL+pPyp/NP637V+bxOaCi+M24/3P/N59niCP/Hyj7Q/Fifzn5Ofl08pTTVNG02fn3Gcufti3YvJlykvF2YL/pT4s+aV5quzf9n+1S8KFE2+Frxe+rv4jcyb42+N3/bMec49fZf4bmG+8L3M+xMf2B/6PgZ8nFrIWsQuVnzS+tT92fXz2FLi0tI/QiyQvpTNDAsAAAAJcEhZcwAACxMAAAsTAQCanBgAAAAddEVYdFNvZnR3YXJlAEdQTCBHaG9zdHNjcmlwdCA5LjI2WJButwAAHdRJREFUeJzt3T9MG2n+x/HHv01xFX+uziDBSlDYFWyD0wFZYV0FSs7RNYHC3uo2xRGgWKJTaAimcQkuLtI1MUhoqzgSSTrsBq7ZoUAnOIlJdQWO6a6aX/FkZ72OMfbYnvnOzPtVRMbjme/j8TzPx/N47MRs21YAAPjt//xuAAAAShFIAAAhCCQAgAgEEgBABAIJACACgQQAEIFAAgCIQCABAEQgkAAAIhBI6Mr79+/9bgKglFLv37+PxWKxWOzg4EApVa1W9Z9ra2t+Nw3tIpDa5Rzu2tjY2Onpqb4zKIPy2tqabm1P2qy39vDhw1gsNjc3V61W9Z2ut7y2tjY8PDw8PMwIgm6cnJwopU5PT4eGhvxuCzpDIHUmk8kcHR1tbW1Vq9VsNut3c9yYmpo6OjqamprqZiN7e3vb29tbW1t6b3z48GFra0sptb29fXR05HqD6+vr6+vr29vbr1696qZ5iKxHjx6dnp4qpbo/yOE9Aqkzw8PDc3Nza2trU1NT//rXv/Sd+/v7+q393t6eUqparc7NzekTKX3q8PU96tczjKZTCg2L9DlNNpvVd+oq9Q+r3+bw8LBzAlf/sOHh4cvLS6XU6enpw4cPndO7rze7t7ent5DNZufm5pruh4uLC6XU3Nyc3htbW1vffvutbu3BwYEu3fRZPH78WDfGKVe/wbW1tbW1taGhIXepBoyNjX348EEpdXp6SiAFj4326CFSnyHt7+8PDQ1NTk7qO2dnZ4+OjkZHR4eGhmzb1ucK+/v7+/v7Sqnd3d2Ge7a2tr6+xyn09SJd5dGjR0dHR5OTk/pV00tXV1d1Y1ZXV+tbODk5qRuzu7tb/zCllH7Y0dFR083q6Y5MJqO3Pzs723RvnJyc6K1NTk5mMpnd3d36da+vr297Fnqn6eZdX1833XLDDgHa4RzY+l/nbY0++FdXV/XD9J/7+/vOMba1tbW/v+9fw/EbAqldDe/Zh4aGTk5OnKPftu3V1VUn4E9OTlZXV2dnZ3V/0KkwOjqqO4Nt27Ozs/rP1dXVoaGh+nH/60VNqzSU0xWde3QMHB0dZTIZnUy2bWcyma8DqelmdVQ8evTotkCybfvi4mJrayuTyYyOjuocsm1bP987n4XTvIZt6tTUmwI64hxgs7Oz+lC3fz0g9fn37u7u7u7u0NDQxcWFfvDFxYVe9PWhCF/c6/4cK1Iymcyf//zn4eFhPRvQ9AP8V69era+vr66u/vDDD3r2IJvNjo2N7e/v609K9KDvyGaz3377bdNyLRbV043Ro3yDarU6PDysbzs37qQfWT/v1+Dg4ODk5MT5pGdubq5QKDTMwjm+fhZNW7K2tqY/l+KiBrhWrVanpqb29vb0Sb82Nja2urqqz9p1ZxwbG5udndX3zM7O3jY1DY/xGVJn9GdIreem9fTd+vq6/sxGKbW2tra7u/vq1atqtTo6Onp5eTk1NVWtVvVn+JeXl/oTIK3Fonp//OMflVLv37+vVqv68x496OtU0KcaU1NT33333X/+85+Dg4PLy0t9OWxreiOvXr26vLx0Auby8nJtbc15OvoefelBtVo9PT29vLzU50l3PgtnGlP9mqOajurJycnr6+u1tbXbsg1obXh4+Lvvvvv8+XNDxqyvr+sbzruo9fX1QqFwcHDgLIL//D5FCwxnPvrrOxtmvZwzFWfKzvnERSmlp7avr6+dd3B6FHa2+fWiplWur6/19pVSo6OjFxcX9q+Tcpr+XKdha+quKTvbtusfr6fs6h/pNPLRo0dOrdHR0ZOTE9u2nY+pbnsWzp26eY76lqvbP7sC3HGm3OsP40wmMzk56WOr0CBm81+Y94E+J2g4kdLze1NTU86E1fv3753ZvwYtFtU7PT3Vl/A13FNfRW9NT1O003Kn8VtbW5eXl7rZe3t7Y2NjDe869YPr26lPmJzq9c/i/fv3Dx8+1ONCm40BemVsbOzx48f6+Ky/AFVfbupv2/AbvxMRslxcXAwNDY2OjupTFufyuYZTQxe+Ps0CvKGvrLm+vtaHd/0Vd5yLi8IZEhpVq9WDg4Nqtfr48eMensdcXl7u7u7+8MMPnBsBaIpAAgCIwFV2AAARCCQAgAgEEgBABAIJACACgQQAEIFAAgCIQCABAEQgkAAAIoT2v5+YmJjwuwkQ5Pz83O8m+IOOgHrCO0JoA0n1btfHYj37PQs25cumIj4ou+gIPdz5FJJTSH5HYMoOACACgQQAEIFAAgCIQCDdrYczwmzKl02hU57tfArJL+QlAgkAIAKBBAAQgUACAIhAIAEARCCQAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQgUACAIhAIAEARCCQAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQgUACAIhAIAEARCCQAAAiEEgAABEIJACACAQSAEAEiYFkmmatVmtzkWVZtz0YiA46AkJAXCAtLS0Vi8Xl5eVyuXznolqttri4ODg46HkzAUHoCAgHWYFUKpUMw9jc3Mzn83t7e3cu2tnZGRgY4I0hIq4nHSG28tGbtSikV/HsGQXIPb8b8DumaSYSCaWUYRiVSqX1okKhMDIyYlkWbwwRZd13BD3M2Tsz/V6LQs5aHrQtiGQFklLKMAx9Y3p6usUi0zRN08zn88fHx7dtKhaL1f9p23ZPWwrR6l/98fFxH1vSV913BOdNd4t33w3jYP0jXaxFodar9KTQb+sGqiPERA3TuVxuZGQknU4rpSYmJs7Pz29bND8/f//+faXUu3fvkslkNpt14kprWB1RFuKD4dmzZ913BM/esFPIy0Jfk98RZJ0hJRIJ0zSVUpZlxePxFosymczNzY1SqlKppFKpgYEBXxoM+KsnHcHemel0lNSP7HSUpJCXhQLJFmZhYWF7e3thYeHt27e2bR8fH4+PjzddpD19+rTpdpy1gCgcDH51BPW3D33dPoV6SH5HkDVlp5XLZcMwGmYe7lzUQP7JKTwT5YMhys8dDeQfDLKm7LRkMuliEQAg0GR9DwkAEFkEEgBABAIJACACgQQAEIFAAgCIQCABAEQgkAAAIhBIAAARCCQAgAgEEgBABAIJACACgQQAEIFAAgCIQCABAEQgkAAAIhBIAAARCCQAgAgEEgBABAIJACACgQQAEIFAAgCIQCABAEQgkAAAIhBIAL6IrXz0YBUKeVwoQAgkAO7ZOzPeDJEUigICCcAX7oZIF2tRyLVwxxiBBOA34RtYJY/gktvmCwIJQLfCly6cJPmCQALwO+EbWCWP4JLb5j0CCUAPhC9d+MjKewQSgEaSB30KeVzISwQSgFt1NOR1M0RSyJtCwhFIAJoI31hMIfkIJAA9E74Jq/AVkoxAAtCcvTOjPJkRopD8Qt4gkAA0EVv56O732fQQSSFvCnVaRTgCCUAT9s5Mp+Ojqpt3an+spFA3hUKWSQQSgFu5G1gp5Fkhd+EnFoEEoBV3X9ukkPBCMsVs2/a7DX0xMTFxfn7udysgQpQPhig/dzSQfzBwhgQAEIFAAgCIQCABAEQgkAAAIhBIAAARCCQAgAgEEgBABAIJACACgQQAEIFAAtDI3Y9VU0h4IfkIJACACAQSgN/x5r/fppAvhYQjkAAAIhBIAAARCCQATXQ0KdTNDBKFvCkUCAQSAEAEAgkAIAKBBOB39P+i3dH/pe1iFddrUchdiUAgkAAEhmcDcSAKhS+WJAaSaZq1Wq2dRaZpWpblVbsAoegICId7fjeg0dLSkmEYZ2dnKysryWTytkXxeHx5eTkej1uWFY/Hnz9/7leDAR/VajU6AkJDViCVSiXDMDY3Ny3L2tjYqA+khkUPHjyYnp7W3W92dpZ+iGja39+nIyA0ZAWSaZqJREIpZRhGpVJpsWhzc1Pff9vkHhAF8/Pz+gYdASEg7jMkwzD0jenp6RaLDMMwDKNcLi8vL2ez2aabiv1e/9oMgSLy0tMR0FqwXnpZZ0hKKeez2YYzpK8X5XK5T58+5fN5J6ga2Lbdt2ZCuvpXf2JiwseW9BsdAS0EqyPICqREImGaplJKf0LbYlGxWNSd0J+GAjLQERAmsgIplUoVCoVcLlepVDKZjFJKz0Wcn583LCqXy5ZlLS0t6RVfv37tY7MBv+gLvukICAdZgaSUOjw8LJfLT5480fMPyWTy/Pz860WpVMrXZgIiOFf3ACEgLpCUUg1fP2pzEQAg0MRdZQcAiCYCCQAgAoEEABAhFtbvKExMTDhXQyDionwwRPm5o4H8g4EzJACACAQSAEAEAgkAIAKBBAAQgUACAIhAIAEARCCQAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQgUACAIhAIAEARCCQAAAiEEgAABEIJACACAQSAEAEAgnArWIrHz1YhUIeFxKLQALQXGzlo70zQyEKeYZAAtAz4RuIw1dIMgIJQBPhG4gpJB+BBKA3wjcQh6+QcAQSgEbhG4gpFAgEEoAeCN9AHL5C8hFIAH4nfAMxhYKCQALQrfANxOErFAj3/G4AACn0Vyw7Gh/djacU8rJQgHCGBECpLt6qd7oihbwvFBQEEoAvwjdPRaFgIZAAuORMH/X7d9so5LpQsBBIAL5wPT66eM/u7uMTCrkrFBQEEoAvb7o9GB+7+UyeQq4LBQVX2QFQypMhlUK+FAqQmG3bfrehLyYmJs7Pz/1uBUSI8sEQ5eeOBvIPBqbsAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQgUACAIhAIAEARCCQAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQgUACAIhAIAEAROhxIBWLxXK53NttAgCioMeBlEwmi8Xis2fParVab7cMAAi3e73dnGEY+Xy+XC4vLy9PT0/rO58/f97bKgCA8OnLZ0ienR6ZpsmpGEBHQDj0+AzJsqyNjY3BwcF//OMfg4ODvd14g6WlJcMwzs7OVlZWkslkX2sBfVWr1Vz3FzoCQqPHZ0jlcjmbzebz+X6nUalUMgxjc3Mzn8/v7e31tRbQbzs7O4uLi4VCodMTnX53hNjKx9jKRxdrUUh4IaHsYNre3n7z5o2+PT4+/vUDmt6JaArEwfDLL79sb2/PzMz8+OOPzrF9J286gvrbBxeruFuLQv0rJL8j9GDKrlgsDgwMGIaxs7Pj3Pn69evut9yaYRj6hnP1RINYLFb/p23b/W4S2hRb+WjvzPS3RN2rPz4+3tdaPZH4VaFQePHixd7e3vz8fDsXBPWkI9z5Fls/oOFVa2ctF6tQqJeFAtURug2kXC5XqVRevnx5c3OjlFpZWSkUCt5MZFuWpW9UKpWmDyCBoqz+1Z+YmPCxJe0ol8ulUundu3fJZDKdTs/PzyulXrx4USwW0+l063V70hFavz9oOtK1s5aLVSjU40KB6gjdBtK7d+8ODw8HBwf192ETiUQ+n19cXLyzF3UpkUiYpqmUsiwrHo/3tRbQb8fHx4lEYmVlpf7D13Q67Zz93MaDjuDidPa2wZFCcgoJ1c183y+//PL06VN9++rqypnLfvr06fHxcTdbbsfCwsL29vbCwsLbt2+/Xjo+Pu5iHhYe8P51kT913o07O0I3G/fsxaKQB4Xkd4SuzpAMw3CmCwzDcM6Kbm5uBgYGuo3KuxweHpbL5SdPntz5LhIIsb52BM/ed1NIfiEPdHXZ9+DgoGEYhUKh/s5isVir1RKJRHcNa0symSSNADoCwqHbz5Dy+fzy8nKpVNJX+FQqlVqtls/ne9E2AECEdBtIg4ODh4eHpVJJf7KayWRSqVQvGgYAiJbe/HRQKpUihwAA3eA/6AMAiEAgAQBEIJAAACIQSAAAEcIcSPbOTHh+lR0Awi7MgQSBwvOjWwB6jUACAIhAIAEARCCQAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQIeSBxI81AEBQhDyQIAo/0wCgBQIJgHIxkRBb+ehuLQp5VihwCCQASnU+3umTXQ8GVgq5LhQ4BBKAL9yNd54NrBRyXSgoCCQAyvlsz8V419GlQxTypVBQEEgAftPpVSd6SHVxrQqFPCsUIAQSgC86/ZqE669VUMizQsFCIAHoimdDJIVCj0ACoNSvE0EeDJEUkl/IL+EPpBC/eIDvwjcWh69QgIQ/kCAEP9MQFOGbsKJQUBBIAHogfGNx+ArJRyABaBS+sZhCgUAgAeiN8I3F4SskHIEEoInwjcUUko9AAtAz4RuLw1dIMgIJQHPhG4spJByBBOBWnv3SGoW8LCQWgQQAEIFAAgCIEIlACtk0axDxMw0A7hSJQAIAyEcgAQBEIJAAACIQSAAAEQgkAIAIBBIAQAQCCQAgAoEEABCBQAIAiBCVQOLHGgBAuKgEEnzE7wYBaAeBBAAQgUACAIhAIAEARCCQAAAiEEgAGrm4JNXdVawU8rKQfAQSAEAEAgkAIAKBBAAQQWIgmaZZq9XaWWSapmVZbW6WH2tAWHXUEQCx7vndgEZLS0uGYZydna2srCSTydsWxePx5eXleDxuWVY8Hn/+/LlfDUZr/ExDX9VqNToCQkNWIJVKJcMwNjc3Lcva2NioD6SGRQ8ePJientbdb3Z2ln6IaNrf36cjIDRkBZJpmolEQillGEalUmmxaHNzU99/2+QeEAXz8/P6Bh0BISArkJRShmHoG9PT0y0W6dvlcnlnZyebzXrZQkAOOgLCxOdAKhaLpVLJ+fObb74ZGRnRtxvOkJRSzse2elEul/v06VM+n3eCqkEsFqv/07btXjUb8tW/+uPj4z62pIca+ksqlUqn03QEtBCsjuBzIKXT6XQ67fxZKpVM01RK6U9o6x+ZSCTqFxWLRd0JW2ycjhdl9a/+xMSEjy3poYb+opSiI6C1YHUEWVN2qVSqUCjkcrlKpZLJZJRS5XJ5eXn5/Py8YVG5XLYsa2lpSa/4+vVrH5sN+EVf8E1HQDjICiSl1OHhYblcfvLkiZ5/SCaT5+fnXy9KpVK+NhMQwbm6BwgBcYGklGr4+lGbiwAAgSbxlxoAABEUrUDi14M8xs80BJHuIx31FOfBLtaiUKeruF5LvmgFEoD+8ez9R/gKQSOQAAAiEEgAuuXZaQSFerWuTAQSgCYCMSJHvFD4EEgAABEIJAC/E74zCdeFOl1RfiHhCCQAvSE/YCAcgQSgkYsR311IUMjLQvIRSAAAESIXSPxYg2f4UiGAjkQukAAAMhFIAAARCCQAgAgEEgBABAIJACACgQQAEIFAAgCIQCABuIOLr+65+7YfhbwsJBCBBKAVyUOq60KdfmU7fIVkimIg8WMNQJt0T+losOsmjTwr1O9VhBcSK4qBBA+E5i1blLkbUl287oEo1O+w9KyQZAQSgCbcjfjO9EP76walUPuEF5KMQALQhB4fPRjvPC6k+v8fN4SvkGcIJAC36jQqXEeLZ4U6Fb5CkhFIAJoI30AsPyzFprJn7vndAAByuRsf+/2/pnpfyAWZhYTjDAlAI/lnLRQK3+mRIpAA9ET4BuLwFZKPQALwO+EbiCkUFBENJH6sAeih8A3E4SsUCBENJPQVfSy4wjcQUyhACCQAXQnfQBy+QkFBIAH4InwDMYWChUAC4F74BuLwFQoQAgnAF/3+nimFfCkUIAQSAEAEAgkAIAKBBAAQgUACAIhAIAEARIhuIPHrQX3CxawA3IluIAEARCGQAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQgUACAIhAIAEARIh0IPFjDT3HzzQAcC3SgQQAkINAAgCIcM/vBviPWTsAkCDqgcQHHgAgBFN2AAARCCQAgAgSA8k0zVqt1uYiy7JuezAQHXQEhIC4QFpaWioWi8vLy+Vy+c5FtVptcXFxcHDQ82YCgtAREA6yAqlUKhmGsbm5mc/n9/b27ly0s7MzMDDAG0NEXE86govLTWMrH92tRSHPCgWLrKvsTNNMJBJKKcMwKpVK60WFQmFkZMSyLN4YIsq67wh6mOv0ilMXv8pBIY8LBY6sQFJKGYahb0xPT7dYZJqmaZr5fP74+Pi2TcVisfo/bdvuaUshWv2rPz4+7mNL+qr7juC86W7x7rthHGxnFXdrUahXhX5bN1AdIebvMF0sFkulkvPnN9988/3336fTaaXUxMTE+fm5syiXy42MjDiL5ufn79+/r5R69+5dMpnMZrNOXGkNqyPKQnMwNPSXVCpVLpe77wjhOzOgUFPyO4LPZ0jpdFpnjFYqlUzTVEpZlhWPx+sfmUgk6hdlMpmbmxulVKVSSaVSAwMD3jYc8EFDf1FKxePx7juC8yvD7Q95+pEu1qKQU6ijgHFRKJBsYRYWFra3txcWFt6+fWvb9vHx8fj4eNNF2tOnT5tux1kLiMLBQEcIHPW3Dx5XlH8w+Dxl11S5XDYMo2Hm4c5FDeSfnMIzUT4Yovzc0UD+wSDuogalVDKZdLEIABBosr6HBACILAIJACACgQQAEIFAAgCIQCABAEQgkAAAIhBIAAARCCQAgAgEEgBABAIJACACgQQAEIFAAgCIQCABAEQgkAAAIhBIAAARCCQAgAgEEgBABAIJACACgQQAEIFAAgCIQCABAEQgkAAAIhBIAAARCCQAgAgE0t1isRibCvSm0CnPdj6F5BfyEoEEABCBQAIAiEAgAQBEiNm27Xcb+mJiYsLvJkCQ8/Nzv5vgDzoC6gnvCKENJABAsDBlBwAQgUACAIhAIAEARCCQAAAihDaQTNOs1Wo9X900TcuyetUSy7I6auRtm7Isq1et6nK/1Wq1TlvSzuoudnuLlnS626PMm33l4vV1USIcT8QRysP4m7///e9+t6H3lpaWLMsqFAqGYRiG0ZPVa7XaX/7yl//+978///zzv//97wcPHnTZklqt9qc//emvf/1rN61SSm1sbJyenv7888//+9//EolE909wZ2fnD3/4Q5ubavDPf/7z5OSkzZ3TzurudnuLlnS626PMg33l+vXtSJcDQju8eSL15cJ5GNuh8/bt259++sm27aurq6dPn/Zq9b29ve3tbX17Zmam+5b89NNPMzMznz9/7mZTx8fH+v7Pnz//+OOP3WzqzZs3+gl+/vzZxX6zbXthYWF8fNzZSz1Z3cVub92SjnZ7xHmwr9y9vh3pckBokwdPpF5YD+N7fgdi75mmqd/dG4ZRqVR6tfr8/Ly+0f5pcouWFAqFkZERy7IGBwe72dTx8fHIyEixWFRK5fP5bjYVj8eLxWK5XD47O4vH4+1sqsHh4WEul3OxYovVXez2Fi3pdLdHmTf7yt3r25EuB4Q2efBEHCE+jMP5GZJzVj49Pd2r1fXJfrlcXl5ezmaz3WzKNE3TNDOZTPetUkq9efNGKXV1dbW0tNTNpgzDGBgYKJVKpVJpZGSko7b1j7vd3pS73R5Nnu2rHr6+ravoG+4GhDZLePBEVNgP4xCeISmlnM8V3b0hum31XC736dOnfD7f/jR0000VCoX79+/ncjnLsjY2NrLZbDsbvK1V8/Pz6XRaKbW4uNhNq/b29lKplN7U7OysviGBi93elLvdHhHFYrFUKjl/3tzcTE9P92NfNRRKpVJXV1c9eX1b6HJAaFOvDtTWwn0YhzCQEomEaZpKKcuyXEw93bZ6sVjUR1v3m8pkMjc3N0qpSqWSSqUGBgZcb2pkZOTq6krfbnOuoMv94zEXu/02LnZ7dKTT6fq3IKZp9mlfNRTq4et7G28OeA+eiBbuwziEgZRKpQqFQi6Xq1QqLk5sG1bX5+Dn5+f6gk5nWuz169euN+VcwDYwMJBMJrtpVTqdXlxczOVyZ2dnbU4U3LapJ0+eLC0tXV1dnZ2dORPifulmt9+2KRe7PbI821fdv7536nJAaJMHT0QL92Ec2h9XLZfL3Vzi2eXqHm/KRYkebgqQjwM7EEIbSACAYAnnVXYAgMAhkAAAIhBIAAARCCQAgAgEEgBABAIJACACgQQAEIFAAhBmpVKpUCgopSzLevbsmd/NQSsEEoAwS6VSpVLJNM2NjQ05PxmMpggkACH38uXL5eXleDwevh9/CxkCCUDIhe8/sgsrAglAyG1sbOTz+Uqlov8fCohFIAEIs1wupyfrXr58+eLFC7+bg1b4tW8AgAicIQEARCCQAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQgUACAIhAIAEARCCQAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQgUACAIhAIAEARPh/qPho3CezhBAAAAAASUVORK5CYII=",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "% 2D object\n",
-    "% simulate frequencies + phase encoding\n",
-    "\n",
-    "N = 8;\n",
-    "Mxy= ones(N+1,N+1);\n",
-    "\n",
-    "x = [-N/2:N/2];\n",
-    "[x,y] = meshgrid(x,x);\n",
-    "Splot = 0.5;\n",
-    "\n",
-    "kPE = [-N/2:N/2]/N; %\n",
-    "dt = 0.1;\n",
-    "Tpe = 1;\n",
-    "\n",
-    "GAMMA = 42.58;\n",
-    "\n",
-    "for Ipe = 1:length(kPE)\n",
-    "    \n",
-    "    for tpe = Tpe %[0:dt:Tpe]\n",
-    "        phase_y = 2*pi*kPE(Ipe)*y *tpe/Tpe;\n",
-    "        \n",
-    "        Mxy_PE = Mxy .* exp(i*phase_y);\n",
-    "        \n",
-    "        figure(Ipe)\n",
-    "        \n",
-    "        subplot(121)\n",
-    "        plot([0:dt:Tpe+dt], [0, ones(1,Tpe/dt)*kPE(Ipe)/(Tpe/dt), 0]), ylim([-0.05 0.05]), ylabel('G_Y') \n",
-    "        title(['Phase encoding, Step ' int2str(Ipe)])\n",
-    "        subplot(122)\n",
-    "        quiver(x-real(Mxy_PE)*Splot/2,y-imag(Mxy_PE)*Splot/2,real(Mxy_PE), imag(Mxy_PE), Splot)\n",
-    "        xlabel('x'), ylabel('y')\n",
-    "        xlim([-N/2-1, N/2+1])\n",
-    "        ylim([-N/2-1, N/2+1])\n",
-    "        title('M_{XY}')\n",
-    "        drawnow\n",
-    "    end\n",
-    "end"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Frequency and Phase Encoding\n",
-    "\n",
-    "The following simulation of the net magnetizations shows how first the phase encoding gradient ($G_Y$) creates some phase variation in $y$, and then during the frequency encoding gradient ($G_X$) the net magnetizations rotate at varying frequencies depending on their $x$ position:\n",
-    "\n",
-    "![frequency_phase_encoding-simple-Mxy.gif](images/frequency_phase_encoding-simple-Mxy.gif)\n",
-    "\n",
-    "Instead of viewing the net magnetizations, we can also visualize this encoding as a map of the phase of the transverse magnetization:\n",
-    "\n",
-    "![frequency_phase_encoding-simple-image_phase.gif](images/frequency_phase_encoding-simple-image_phase.gif)\n",
-    "\n",
-    "(See ``spatial_encoding_Mxy_illustration.m`` for code generating this movie)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## K-space Trajectories\n",
-    "\n",
-    "K-space is a very general method for capturing the effect of spatial encoding gradients, and the \"k-space trajectory\" is defined as the pattern created over time by the gradients:\n",
-    "\n",
-    "$$\\vec{k}(t) = \\frac{\\gamma}{2\\pi} \\int_0^t \\vec{G}(\\tau) d\\tau$$\n",
-    "\n",
-    "Note that k-space trajectories always start at the center of k-space, $\\vec{k}(0) = 0$ and are only defined once there is transverse magnetization (e.g. after an RF pulse).\n",
-    "\n",
-    "The following simulation of the net magnetizations shows how rotations and k-space trajectory during a typical Cartesian (or 2D FT) gradient pulse sequence, which is differs from the simulation above in that an initial dephasing gradient in the frequency encoding direction is applied to sample both positive and negative spatial frequencies in k-space:\n",
-    "\n",
-    "![frequency_phase_encoding-full-Mxy.gif](images/frequency_phase_encoding-full-Mxy.gif)\n",
-    "\n",
-    "![frequency_phase_encoding-full-image_phase.gif](images/frequency_phase_encoding-full-image_phase.gif)\n",
-    "\n",
-    "(See ``spatial_encoding_Mxy_illustration.m`` for code generating this movie)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### K-space trajectories\n",
-    "\n",
-    "The k-space pattern during a MRI experiment is referred to as the k-space \"trajectory\".  The most common are Cartesian trajectories, in which parallel lines of k-space are covered to sample a 2D (or 3D) grid.  K-space trajectories with other patterns, such as radial lines, spirals, rastered lines (echo-planar trajectories), or blades can also be used. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjAAAAGkCAIAAACgjIjwAAAJMmlDQ1BkZWZhdWx0X3JnYi5pY2MAAEiJlZVnUJNZF8fv8zzphUASQodQQ5EqJYCUEFoo0quoQOidUEVsiLgCK4qINEWQRQEXXJUia0UUC4uCAhZ0gywCyrpxFVFBWXDfGZ33HT+8/5l7z2/+c+bec8/5cAEgiINlwct7YlK6wNvJjhkYFMwE3yiMn5bC8fR0A9/VuxEArcR7ut/P+a4IEZFp/OW4uLxy+SmCdACg7GXWzEpPWeGjy0wPj//CZ1dYsFzgMt9Y4eh/eexLzr8s+pLj681dfhUKABwp+hsO/4b/c++KVDiC9NioyGymT3JUelaYIJKZttIJHpfL9BQkR8UmRH5T8P+V/B2lR2anr0RucsomQWx0TDrzfw41MjA0BF9n8cbrS48hRv9/z2dFX73kegDYcwAg+7564ZUAdO4CQPrRV09tua+UfAA67vAzBJn/eqiVDQ0IgALoQAYoAlWgCXSBETADlsAWOAAX4AF8QRDYAPggBiQCAcgCuWAHKABFYB84CKpALWgATaAVnAad4Dy4Aq6D2+AuGAaPgRBMgpdABN6BBQiCsBAZokEykBKkDulARhAbsoYcIDfIGwqCQqFoKAnKgHKhnVARVApVQXVQE/QLdA66At2EBqGH0Dg0A/0NfYQRmATTYQVYA9aH2TAHdoV94fVwNJwK58D58F64Aq6HT8Id8BX4NjwMC+GX8BwCECLCQJQRXYSNcBEPJBiJQgTIVqQQKUfqkVakG+lD7iFCZBb5gMKgaCgmShdliXJG+aH4qFTUVlQxqgp1AtWB6kXdQ42jRKjPaDJaHq2DtkDz0IHoaHQWugBdjm5Et6OvoYfRk+h3GAyGgWFhzDDOmCBMHGYzphhzGNOGuYwZxExg5rBYrAxWB2uF9cCGYdOxBdhK7EnsJewQdhL7HkfEKeGMcI64YFwSLg9XjmvGXcQN4aZwC3hxvDreAu+Bj8BvwpfgG/Dd+Dv4SfwCQYLAIlgRfAlxhB2ECkIr4RphjPCGSCSqEM2JXsRY4nZiBfEU8QZxnPiBRCVpk7ikEFIGaS/pOOky6SHpDZlM1iDbkoPJ6eS95CbyVfJT8nsxmpieGE8sQmybWLVYh9iQ2CsKnqJO4VA2UHIo5ZQzlDuUWXG8uIY4VzxMfKt4tfg58VHxOQmahKGEh0SiRLFEs8RNiWkqlqpBdaBGUPOpx6hXqRM0hKZK49L4tJ20Bto12iQdQ2fRefQ4ehH9Z/oAXSRJlTSW9JfMlqyWvCApZCAMDQaPkcAoYZxmjDA+SilIcaQipfZItUoNSc1Ly0nbSkdKF0q3SQ9Lf5RhyjjIxMvsl+mUeSKLktWW9ZLNkj0ie012Vo4uZynHlyuUOy33SB6W15b3lt8sf0y+X35OQVHBSSFFoVLhqsKsIkPRVjFOsUzxouKMEk3JWilWqUzpktILpiSTw0xgVjB7mSJleWVn5QzlOuUB5QUVloqfSp5Km8oTVYIqWzVKtUy1R1WkpqTmrpar1qL2SB2vzlaPUT+k3qc+r8HSCNDYrdGpMc2SZvFYOawW1pgmWdNGM1WzXvO+FkaLrRWvdVjrrjasbaIdo12tfUcH1jHVidU5rDO4Cr3KfFXSqvpVo7okXY5upm6L7rgeQ89NL0+vU++Vvpp+sP5+/T79zwYmBgkGDQaPDamGLoZ5ht2GfxtpG/GNqo3uryavdly9bXXX6tfGOsaRxkeMH5jQTNxNdpv0mHwyNTMVmLaazpipmYWa1ZiNsulsT3Yx+4Y52tzOfJv5efMPFqYW6RanLf6y1LWMt2y2nF7DWhO5pmHNhJWKVZhVnZXQmmkdan3UWmijbBNmU2/zzFbVNsK20XaKo8WJ45zkvLIzsBPYtdvNcy24W7iX7RF7J/tC+wEHqoOfQ5XDU0cVx2jHFkeRk4nTZqfLzmhnV+f9zqM8BR6f18QTuZi5bHHpdSW5+rhWuT5z03YTuHW7w+4u7gfcx9aqr01a2+kBPHgeBzyeeLI8Uz1/9cJ4eXpVez33NvTO9e7zofls9Gn2eedr51vi+9hP0y/Dr8ef4h/i3+Q/H2AfUBogDNQP3BJ4O0g2KDaoKxgb7B/cGDy3zmHdwXWTISYhBSEj61nrs9ff3CC7IWHDhY2UjWEbz4SiQwNCm0MXwzzC6sPmwnnhNeEiPpd/iP8ywjaiLGIm0iqyNHIqyiqqNGo62ir6QPRMjE1MecxsLDe2KvZ1nHNcbdx8vEf88filhICEtkRcYmjiuSRqUnxSb7JicnbyYIpOSkGKMNUi9WCqSOAqaEyD0tandaXTlz/F/gzNjF0Z45nWmdWZ77P8s85kS2QnZfdv0t60Z9NUjmPOT5tRm/mbe3KVc3fkjm/hbKnbCm0N39qzTXVb/rbJ7U7bT+wg7Ijf8VueQV5p3tudATu78xXyt+dP7HLa1VIgViAoGN1tubv2B9QPsT8M7Fm9p3LP58KIwltFBkXlRYvF/OJbPxr+WPHj0t6ovQMlpiVH9mH2Je0b2W+z/0SpRGlO6cQB9wMdZcyywrK3BzcevFluXF57iHAo45Cwwq2iq1Ktcl/lYlVM1XC1XXVbjXzNnpr5wxGHh47YHmmtVagtqv14NPbogzqnuo56jfryY5hjmceeN/g39P3E/qmpUbaxqPHT8aTjwhPeJ3qbzJqamuWbS1rgloyWmZMhJ+/+bP9zV6tua10bo63oFDiVcerFL6G/jJx2Pd1zhn2m9az62Zp2WnthB9SxqUPUGdMp7ArqGjzncq6n27K7/Ve9X4+fVz5ffUHyQslFwsX8i0uXci7NXU65PHsl+spEz8aex1cDr97v9eoduOZ67cZ1x+tX+zh9l25Y3Th/0+LmuVvsW523TW939Jv0t/9m8lv7gOlAxx2zO113ze92D64ZvDhkM3Tlnv296/d5928Prx0eHPEbeTAaMip8EPFg+mHCw9ePMh8tPN4+hh4rfCL+pPyp/NP637V+bxOaCi+M24/3P/N59niCP/Hyj7Q/Fifzn5Ofl08pTTVNG02fn3Gcufti3YvJlykvF2YL/pT4s+aV5quzf9n+1S8KFE2+Frxe+rv4jcyb42+N3/bMec49fZf4bmG+8L3M+xMf2B/6PgZ8nFrIWsQuVnzS+tT92fXz2FLi0tI/QiyQvpTNDAsAAAAJcEhZcwAACxMAAAsTAQCanBgAAAAddEVYdFNvZnR3YXJlAEdQTCBHaG9zdHNjcmlwdCA5LjI2WJButwAAFMBJREFUeJzt3cFrm3me4OHXO4Huk2MXbB+GvKHjhvHBgmErdbHrslQ5ENEsC6FiN81C2wc5p6b2kMQZqBTF+jBJKYfxMdYhOeyhZS9NDwOtgF3DnqRL3MuA0uBpqgKlYg69YLfyD2gP745QEttJHL3WV/LznORXr97390Ylfer3vrI81ul0EgAYtP8w6AEAQJIIEgBBCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSo+/g4GB3d3fQowDeQJAYZbu7u/Pz8x988MFHH300OTm5sbHxNo9aXV3d2dl5y13s7OyMjY29/fon2NG77uKdxg9xCBKj7Pr167u7uw8fPtze3p6amrpx48bbTJW+/vrr7e3tt9zF5cuXt7e3L1++fILhveWO3nUX7zR+iEOQGFlbW1vPnz+/c+fOysrK/Pz81tbWp59+uru7e3BwMD8/PzY2NjY2Nj8/f3BwkE1BVldXJycnV1dXs8dm6VpdXc3WzJa//tjd3d0rV64cs9mVlZVs4Svzs94d9Q7gmF28Pp7eJdnKr49/cnJybGxsamoqW9K7r/n5+cnJyWw7ly9fPllWoW86MKJu376dJMn29vYry+/du5ckyebm5ubmZpIk2fwpSZJLly7dvn376dOnSZKUSqX9/f1X1rx3797rS7LHbm9vH7XZzz77bHt7+8MPP3zl5da7o94BHLWd13dx79697Mbt27c3NzcnJiZeGX/2wFKplA1gYmKi0+n07uvhw4dJkjx9+nR/fz/b4Ok9PfCac6fUPQhjdXV1fn5+c3MzmzF8++23U1NTSZLcv3//+vXr2TqTk5OTk5Pb29uXLl3K3uInJia2t7cXFhayLVy/fn1zc/P69evdqzVHbfbGjRvz8/Pz8/N/+MMfeoeRTUeyHWVLugM4dDtJkrw+nmwj9+/fT5IkW613s1l7spnZnTt3FhYWuqPN9nVwcHDjxo3Nzc2f/exnSZKsrKzk8O8Nb8spO0bWRx99lCTJd999l/343Xffzc/Pb2xs3L9/P7vrxo0bvet3w3ColZWVhYWFlZWV7e3tbDsLCwvd82ZJkhy12beXDeAtt5ONp3fJO51zy/Y1OTlZKpW2traePn362WefHf8vAHkTJEbW/Pz8xMTE6urq1tbWzs7OvXv3vvnmm6mpqWyecefOnW6rjnL58uWDg4M7d+5kK2dXaB4+fHj//v2Dg4NLly71buHtN3u8Y7bz+ng++OCDJEl2dnYODg6mpqZemeJk855shpSd03u9WFeuXHn+/PnW1taVK1feZ9jQB4M+Zwg5evr06aVLl7r/tT98+LDT6WTXXZIk+fTTT5MkuX37dvciTfaoiYmJ7Mf9/f3s2k+SJB9++OH+/v7Tp0+ze5N/P2nWfezxm80uaL0yvO6Oetc8Zjuvj2d/fz9bLUmSS5cuffvtt72b7XQ6pVLplcN/5WC76+/v75/GUwJHG+v4E+aMuuwjcJcvX+6eksqmF0ed4Mo+2NZdf2dnZ3Jysnfl7EpM7wbfZrNv3NFR29nZ2bly5Up2qvDQ8XQ/43foZl8//Fdkn7Xb2tp6y2FDTgQJopuamnr+/Hk3SP01Pz//zTff5LRxeCc+ZQfR3blzJ/udoTw2fvny5fv37/sNJCIwQwIgBJ+yAyAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIghIjf1DA9PT3oIQBwcnt7eyd4VMQgJSc9mKE2NnYWvzXDUZ8djvrsOPGkwik7AEIQJABCECQAQhCkKM7giebEUZ8ljpo3EiQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCODfoAcTyr9f/etBDAOiPv9n6t0EP4d2YIQEQgiABEIIgARCCa0gvGbpTrgAjwwwJgBAECYAQBAmAEAQJgBAECYAQBAmAEAQJgBAECYAQBAmAEAQJgBAECYAQBAmAEAQJgBAECYAQBAmAEAQJgBAECYAQBAmAEAQJgBAECYAQBAmAEPINUrPZbLfbh97VarWOuguAMyjHIC0tLVWr1eXl5Xq9/spd7Xb72rVr58+fz2/vAAyXvIJUq9XSNF1bW1tfX9/Y2Hjl3gcPHoyPj5shAdCVV5CazWahUEiSJE3TRqPRe1elUrl48WKapmZIAHTleMouTdPsxuzsbHdhs9lsNpulUun4x471yG+EAPRFX960cwxSq9XKbvTOkCqVyoULF8rlcqvVunv3bnedV3R65DdCAPqiL2/a5/o4oF6FQqHZbCZJ0mq1ZmZmustLpdKLFy+SJGk0GsVicXx8PKcBADBc8gpSsVisVCrlcrnRaGQn6Or1+vLy8t7eXrbC+Pj43NxcTnsHYOiM5XpOrF6vp2navZj0lqanp7vdAmC4nPg9PK8ZUsYcCIC3lG+Qhs7YzX8e9BAA+qPz4JNBD+Hd+C47AEIQJABCECQAQnAN6SVDd8oVYGSYIQEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQwrlBDyCW//kf/3bQQwDoj//2f/9l0EN4N2ZIAIQgSACEIEgAhOAa0kuG7pQrwMgwQwIgBEECIARBAiAEQQIgBEECIARBAiAEQQIghHyD1Gw22+32octbrVauuwZguOT4i7FLS0tpmj579uzmzZtzc3PZwna7vby8PDMz02q1ZmZmbt26ld8AABgiec2QarVamqZra2vr6+sbGxvd5Zubm7Ozs2tra48fP37y5ElOewdg6OQ1Q2o2m4VCIUmSNE0bjUZ3+dWrV7Mbh57KA+DMyvEaUpqm2Y3Z2dnehWma1uv15eXllZWVox471iO/EQLQF315087xGlL3Ywu9M6QkScrl8g8//LC+vt4t1us6nU5+AwOgv3rftKenp0+2kbyCVCgUms1mkiTZhxe6y6vValajnPYLwJDKK0jFYrFSqZTL5UajUSqVkiTJTtMtLCy0Wq2lpaVstcePH+c0AACGy1iuJ8fq9Xp20eidHjU9Pb23t5fTkADI1Ynfw/P9A33dXz8CgOP56iAAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAELI989PDJ3/8r/3Bz0EgP74p//8waCH8G7MkAAIQZAACEGQAAjBNaSXDN0pV4CRYYYEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAhvCFKr1TqdcQBwxr0hSL/5zW+WlpYqlUp/y9RsNtvtdh83CMCwG+t0Om9cqVarPXnyJEmSubm5xcXF99zl0tJSmqbPnj27efPm3Nzc6ytMT0/v7e29514AGIgTv4e/YYbUbrer1eqTJ09arVahUHjx4sXnn39+ohH+f7VaLU3TtbW19fX1jY2N99kUAKPk3PF3b2xsTExM3Lx5M03TbEmtVnuf/TWbzUKhkCRJmqaNRuN9NpWHv/tf/2nQQwDoj7//7P8Megjv5g0zpFu3bs3MzHRrlCRJsVh8z112tzY7O3vUOmM93nN3AOStL2/ahwSpXC5nnzhot9vlcvnu3bsnH+Nhup+POGaG1OnR370D0Hd9edM+JEgXL15cXl6uVqvz8/NJkvz2t789+RhfUygUvv/++yRJWq3WzMxMH7cMwFA7/FN21Wr1yy+/fPTo0aGfgntP165dm52dbTQapVLp0BOAPmUHMLxO/B7+UpDK5XL3dnY+LbvMc+vWrfce4Uvq9Xqapr2XpnoJEsDwOvF7+Eufsvv4448Pvd13eUy8ABhqLwVJJwAYFF+uCkAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAI5wY9gFi+/Nt/GPQQAPrjf/zLfx/0EN6NGRIAIQgSACEIEgAhuIb0kqE75QowMsyQAAhBkAAIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAIId8gNZvNdrt96PJWq5XrrgEYLjn+PaSlpaU0TZ89e3bz5s25ublsYbvdXl5enpmZabVaMzMzt27dym8AAAyRvGZItVotTdO1tbX19fWNjY3u8s3NzdnZ2bW1tcePHz958iSnvQMwdPKaITWbzUKhkCRJmqaNRqO7/OrVq9mNQ0/lAXBm5XgNKU3T7Mbs7GzvwjRN6/X68vLyysrKUY8d65HfCAHoi768afdnhlStVmu1WvfHYrGYJEn3Ywu9M6QkScrl8g8//LC+vt4t1us6nU5fBgbAKeh9056enj7ZRvoTpMXFxcXFxd4ltVqt2WwmSZJ9eKG7vFqtZjXqy34BGBl5XUMqFouVSqVcLjcajVKplCRJdppuYWGh1WotLS1lqz1+/DinAQAwXMZyPTlWr9ezi0bv9Kjp6em9vb2chgRArk78Hp7j7yElSdL99SMAOJ6vDgIgBEECIARBAiAEQQIgBEECIARBAiAEQQIghHx/D2no7P/j1KCHANAfH/zX7wY9hHdjhgRACIIEQAiCBEAIriG9ZOhOuQKMDDMkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEI4N+gBxPKv1/960EMA6I+/2fq3QQ/h3ZghARCCIAEQgiABEIJrSC8ZulOuACMj3xlSs9lst9uH3tVqtY66C4AzKMcgLS0tVavV5eXler3+yl3tdvvatWvnz5/Pb+8ADJe8glSr1dI0XVtbW19f39jYeOXeBw8ejI+PmyEB0JVXkJrNZqFQSJIkTdNGo9F7V6VSuXjxYpqmZkgAdOV4yi5N0+zG7Oxsd2Gz2Ww2m6VS6fjHjvXIb4QA9EVf3rT78ym7arVaq9W6PxaLxSRJWq1W9mPvDKlSqVy4cKFcLrdarbt3766srHS71avT6fRlYACcgt437enp6ZNtpD9BWlxcXFxc7F1Sq9WazWaSJK1Wa2Zmpru8VCq9ePEiSZJGo1EsFsfHx/syAACGXV6/h1QsFiuVSrlcbjQa2Qm6er2+vLy8t7eXrTA+Pj43N5fT3gEYOmO5nhyr1+tpmh56Uu4Y09PT3W4BMFxO/B6e7zc1mAMB8JZ8lx0AIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhnBv0AGIZu/nPgx4CQH90Hnwy6CG8GzMkAEIQJABCECQAQnAN6SVDd8oVYGSYIQEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQgiABEIIgARCCIAEQgiABEIIgARCCIEUxNjY26CEMgKM+Oxw1byRIAIQgSACEIEgAhCBIAIQw1ul0Bj2GV01PTw96CACc3N7e3gkeFTFIAJxBTtkBEIIgARCCIAEQgiANXrPZbLfbh97VarWOumvYHXPUzWaz1Wqd8nhO0zHHPmKOOtLRforP5iu6L/7qq6++GvQYzrSlpaVWq1WpVNI0TdO09652u/3zn//817/+9aDGlp+jjrrdbv/yl7/885///Lvf/e5Pf/rTxx9/PMBB5uSYZ3zEHHqkI/8Un81XdN90GJzf//73X3zxRafT+f7773/1q1+9cu8XX3zxySef/OUvfxnAyPJ0zFFvbGx8/fXX2e1PPvnk9MeWt+Of8VFy1JGO9lN8Nl/RfXRu0EE805rNZqFQSJIkTdNGo9F7V6VSuXjxYqvVOn/+/IBGl5djjvrq1avZjVE9rXHMsY+Yo450tJ/is/mK7iPXkAasO6mfnZ3tLmw2m81ms1QqDWhQuTv0qLPlaZrW6/Xl5eWVlZVBDC13Rx376Dn0SEf+KT6br+h+MUM6PdVqtVardX8sFotJknQv7fb+/1SlUrlw4UK5XG61Wnfv3l1ZWRneiw1vf9SZcrn8ww8/rK+vD+8hH++YYx8xRx3paD/FI/+KzpUgnZ7FxcXFxcXeJbVardlsJknSarVmZma6y0ul0osXL5IkaTQaxWJxfHz8lIfaR29/1EmSVKvV7K3qVId4igqFwlHHPmKOOtLRfoqPOupRekXnylcHDdi1a9dmZ2cbjUapVCoWi9mpjO7XQC0tLT1+/HigA8zFUUd99+7dZ8+edV+uZ+HYBz2cHPUe6fnz58/IU3zoUXfvHdVXdL8I0uDV6/WR/wTw687mUWfOzrGfnSPtdTaPui8ECYAQfMoOgBAECYAQBAmAEAQJgBAECYAQBAlOQ71eL5fLgx4FhCZIAIQgSHCqqtWqqRIcynfZwempVqvVavXRo0eDHghEZIYEp6TRaHz55ZeLi4v+Ig4cSpDg9Dx69OjBgwcj+bfp4P391VdffTXoMcDoa7VanU7nF7/4Rbvd3t3d/eMf//ijH/3oJz/5SblcLhQKP/7xjwc9QBg8MyQ4VSsrK0+ePPnpT3/64MGDSqVSKBScwYOMb/uGwcj+lq6/jgNdZkgwGLVa7fz589kfGAUSMyQYiOzS0dzc3Oeff26SBBlBAiAEp+wACEGQAAhBkAAIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAIQZAACOH/AaYS1VPt03mHAAAAAElFTkSuQmCC",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "%  plot 2D k-space trajectories\n",
-    "\n",
-    "% Cartesian\n",
-    "N = 8;\n",
-    "\n",
-    "k = [-N/2:N/2]/N;\n",
-    "[ky,kx] = meshgrid(k,k);\n",
-    "\n",
-    "figure\n",
-    "plot(kx, ky, 'LineWidth',10), xlim([-.6 .6]), ylim([-.6 .6])\n",
-    "xlabel('k_x'),ylabel('k_y')\n",
-    "title('Cartesian trajectory')\n",
-    "\n",
-    "% echo-planar\n",
-    "kx_ep = kx; kx_ep(:,2:2:end) = kx_ep(end:-1:1,2:2:end);\n",
-    "kx_ep = kx_ep(:);\n",
-    "\n",
-    "ky_ep = ky(:);\n",
-    "\n",
-    "figure\n",
-    "plot(kx_ep, ky_ep, 'LineWidth',10), xlim([-.6 .6]), ylim([-.6 .6])\n",
-    "xlabel('k_x'),ylabel('k_y')\n",
-    "title('Echo-Planar trajectory')\n",
-    "\n",
-    "% radial\n",
-    "\n",
-    "k_theta = exp(i*2*pi*[1:N]/(2*N));\n",
-    "k_radial = k.' * k_theta;\n",
-    "\n",
-    "figure\n",
-    "plot(real(k_radial), imag(k_radial), 'LineWidth',10), xlim([-.6 .6]), ylim([-.6 .6])\n",
-    "xlabel('k_x'),ylabel('k_y')\n",
-    "title('Radial trajectory')\n",
-    "\n",
-    "\n",
-    "% spiral\n",
-    "n = linspace(0,1,201);\n",
-    "Nturns = N/2;\n",
-    "k_spiral = 1/2*n.*exp(i*2*pi*Nturns*n);\n",
-    "\n",
-    "figure\n",
-    "plot(real(k_spiral), imag(k_spiral), 'LineWidth',10), xlim([-.6 .6]), ylim([-.6 .6])\n",
-    "xlabel('k_x'),ylabel('k_y')\n",
-    "title('Spiral trajectory')\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "vscode": {
-     "languageId": "javascript"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "%  plot 3D k-space trajectories\n",
-    "\n",
-    "% Cartesian\n",
-    "N = 8;\n",
-    "\n",
-    "k = [-N/2:N/2]/N;\n",
-    "[ky,kx,kz] = meshgrid(k,k,k);\n",
-    "\n",
-    "\n",
-    "figure\n",
-    "plot3(reshape(kx, [N+1 (N+1)^2]), reshape(ky, [N+1 (N+1)^2]), reshape(kz, [N+1 (N+1)^2]), 'LineWidth',10)\n",
-    "xlim([-.6 .6]), ylim([-.6 .6]), zlim([-.6 .6])\n",
-    "xlabel('k_x'),ylabel('k_y'), zlabel('k_z')\n",
-    "title('Cartesian trajectory')\n",
-    "\n",
-    "% radial\n",
-    "\n",
-    "N_radial = N^3;\n",
-    "\n",
-    "n = 1:N_radial;\n",
-    "\n",
-    "kz = (2*n - N_radial - 1) / N_radial;\n",
-    "kx = cos(sqrt(N_radial*pi) .* asin(kz)) .* sqrt(1-kz.^2);\n",
-    "ky = sin(sqrt(N_radial*pi) .* asin(kz)) .* sqrt(1-kz.^2);\n",
-    "\n",
-    "figure\n",
-    "plot3([zeros(1,N_radial); kx], [zeros(1,N_radial); ky], [zeros(1,N_radial); kz])\n",
-    "xlim([-.6 .6]), ylim([-.6 .6]), zlim([-.6 .6])\n",
-    "xlabel('k_x'),ylabel('k_y'), zlabel('k_z')\n",
-    "title('Radial trajectory')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "These movies illustrate the phase accumulation during non-Cartesian trajectories\n",
-    "\n",
-    "![radial_encoding-full-Mxy.gif](images/radial_encoding-full-Mxy.gif)\n",
-    "\n",
-    "![spiral_encoding-full-Mxy.gif](images/spiral_encoding-full-Mxy.gif)\n",
-    "\n",
-    "(See ``spatial_encoding_Mxy_illustration.m`` for code generating this movie)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
diff --git a/build_notes.html b/build_notes.html
index 4a644ae..e906740 100644
--- a/build_notes.html
+++ b/build_notes.html
@@ -189,7 +189,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/genindex.html b/genindex.html
index f94235e..f2a1068 100644
--- a/genindex.html
+++ b/genindex.html
@@ -188,7 +188,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/objects.inv b/objects.inv
index c86505aedc7b15a004b3c845f02bc31241a0bb83..68584b478063f796e15f174c989824e504de5dcf 100644
GIT binary patch
delta 687
zcmV;g0#N;)2AKwsc7IE6+b|5i>sRP9pgnllb{vKcZP5%tkt}nHUJF%bVgZWe+A^~I
z`;mG$mhEAO*ap9cNJ?Vvqy!DEa8U8}NgS0q@(sA!RvqtL^|i8+7oYjvmG<Gwr%1%F
zNc~v5lja4xYn?g>>2hrfCf4fL3m2y1C3IHzPFXXiBZ|g|<A3wY2-=kbU2%KhFAC25
z2C26bC$<uu8!FlLx&yw4_a2OdEGyz=rFbsB2lkL|Z}?fcnwP6!nEUhwMTAqnt7H__
zbL|iIvlW#B<9z1(Mj8GnYn!_!&d>?s;VUqM_p;BlW=0hPc1T*&xwe<netX>addx`0
zuZ?SMwV)cs1AjMTI?SV0Myf_*VYp$Na?PHKt`QQ(HZhb|dx8rw`GdvOoBS9dMhC83
z<1^twH&anV9^ZRGsdQ{p@?CxDl<auH@3ocn0FM1PCGA}x;#Yw`Po}O%dRQ*EU~y&F
z(!tC8Vx}HR6%u<R@IWk;7$gMGY7EM)bqjfuC?SEJaet{B&(NNfvDzLl-e|9mM(BU^
zf&2ntR{L`ed`VAh#Jvpum(Iay!PdtoUOvV);%LAr87_I)M7%W*R_VM+k%w-9d7Tz3
z-!|mOE+of8aKsxz$1uMjW9#V%xaOH_*zX=Xf4Ii#A$Z+`A;cDE$81~_EH)PJ&(<nj
zvZVfwHGjj#IP14v`HVd+cq}{I?6>7D+uMUXixysKVD{}~B+k)mB?;pL#`X<5(;+a@
zRy1wLRso~)6Vai-1|;4HT_pKpXQr&B*-BoxrRi>GYCkL^lGty(($%Z6E?;UC4$N=H
za;Kbz@9YRhnF{`Rz7}twNs*#y?%^jpQIRudb0{ei5L<~8QbW{?(ErGG7yO$wxw-?<
V;vC9^Ar{X;z;`&^*<XZNt~p7(S1JGi

delta 692
zcmV;l0!#gw2A&3xc7Mrk+b|Hl^DB5MkQ`LBJr+faB!~+maO%oIt^q@hEdn&Dh!j%)
zeP_7HqO76^+rqp>vykH(DM3RoJT!cL6bEGvd;`9<jpNQYUmGiV^_kzCX&=6PN<@50
z)Q_z{YF@FM-mATkzSQPmX03ibb72}@gR^?@%9<%1Q8Y#zzkkn+s9h=04Yzy#tl*tr
zA@zFZ#8$%jv6Ahe9q=8z4PYb`SrM-&C2;X~WRK|%hQBM{@_H2wOP|4@h;Yhxm5q}6
zQu~Ab>_wx%_>lRoQ-<Hm)|RfBGj@V__!F7Yd)a4RGouOtJ0z`fz8~bg-vJN3o-%Ur
zYvX&{ET|^&$bT)E9`opxk*d>J7!GVxuh~Q8Iw4_dlS0uU<M&3|28Y5P;6y@xXR(s5
zJXMI%`K#CXo$+KdS5bfN-v&XMIku_!wmmr|9k2MUwz3_;ssE;?QAQ#@Rrm>H8bYGS
z*OeA5z1jD44hz4OX+Uy&iM<hcK9)+15`r&kjLJvr7k~05QAQ%W;8Hi9pg$^OwLP4I
z(M}zV(EsQI`9;D-?N2T6B|W_(O*8tRoQLCrZHUjjLX2(1!GKpX-uXC0yhL|a>9R?Q
zhi;L1ULLE^Hsq%+WXFAU#0x{Gvb--->-k1F=UHml?*UvmTvPQJJkMYZvBgz#u{|o5
z8jIKI(SIs@WljB^YR18M8^*3e#(@?+mL0BkkM%X%*}Z=kJ-pEV9QxUYyhP8HWQ>m(
z+jZznhalbF!YX2PeiAws*nz|wp{p!k?980Cv}(x<N1E?;p$@w<A({O;DBZjm>&sV7
z!jbvSSnieA@SPpNDAT~7z}MmxG%0d4uR(ldM=dJyg4vy_45U`#!qkv76ZAi_?Fs*N
aO{sPudfY>WFvik3i1-$lJ^KsETC>+MAYU~A

diff --git a/reports/Spatial Encoding.err.log b/reports/Spatial Encoding.err.log
deleted file mode 100644
index 8e62f4a..0000000
--- a/reports/Spatial Encoding.err.log	
+++ /dev/null
@@ -1,59 +0,0 @@
-Traceback (most recent call last):
-  File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_cache/executors/utils.py", line 58, in single_nb_execution
-    executenb(
-  File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 1305, in execute
-    return NotebookClient(nb=nb, resources=resources, km=km, **kwargs).execute()
-  File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_core/utils/__init__.py", line 165, in wrapped
-    return loop.run_until_complete(inner)
-  File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/asyncio/base_events.py", line 616, in run_until_complete
-    return future.result()
-  File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 705, in async_execute
-    await self.async_execute_cell(
-  File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 1058, in async_execute_cell
-    await self._check_raise_for_error(cell, cell_index, exec_reply)
-  File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 914, in _check_raise_for_error
-    raise CellExecutionError.from_cell_and_msg(cell, exec_reply_content)
-nbclient.exceptions.CellExecutionError: An error occurred while executing the following cell:
-------------------
-% simulate frequency encoding
-N = 8;
-Mxy= ones(N+1,N+1);
-
-x = [-N/2:N/2];
-[x,y] = meshgrid(x,x);
-Splot = 0.5;
-
-kFE = 1/2;
-dt = 0.1;
-Tfe = 2;
-
-GAMMA = 42.58;
-
-
-for tfe = linspace(0,1,6)*Tfe
-    phase_x = 2*pi*kFE*x *tfe/Tfe;
-        
-    Mxy_FE = Mxy .* exp(i*phase_x);
-        
-    figure
-    subplot(121), plot([0:dt:Tfe+dt],  [0, ones(1,Tfe/dt)*kFE/(Tfe/dt), 0], tfe*ones(1,2), [-0.05 0.05]), ylabel('G_X')
-    title('Frequency Encoding')
-    subplot(122)
-    quiver(x-real(Mxy_FE)*Splot/2,y-imag(Mxy_FE)*Splot/2,real(Mxy_FE), imag(Mxy_FE), Splot)
-    xlabel('x'), ylabel('y')
-    xlim([-N/2-1, N/2+1])
-    ylim([-N/2-1, N/2+1])
-    title('M_{XY}')
-    drawnow
-end
-
-
-------------------
-
-
-  Cell In[1], line 5
-    x = [-N/2:N/2];
-             ^
-SyntaxError: invalid syntax
-
-
diff --git a/search.html b/search.html
index daf8dcb..44da947 100644
--- a/search.html
+++ b/search.html
@@ -190,7 +190,7 @@
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Formation</span></p>
 <ul class="nav bd-sidenav">
 <li class="toctree-l1"><a class="reference internal" href="Spatial%20Encoding.html">Spatial Encoding</a></li>
-<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space Encoding</a></li>
+<li class="toctree-l1"><a class="reference internal" href="K-space.html">K-space</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Image%20Reconstruction.html">Image Reconstruction</a></li>
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Image Characteristics</span></p>
diff --git a/searchindex.js b/searchindex.js
index f785d44..b53e008 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"docnames": ["Accelerated Imaging Methods", "Artifacts", "FOV and Resolution", "Fast Imaging Pulse Sequences", "Fun with RF Pulses", "Gradient and Spin Echoes", "Image Reconstruction", "Introduction", "K-space", "Key MRI Concepts", "MR Physics - Bloch Equation", "MRI Contrast", "MRI Math Concepts", "MRI Notation", "MRI Signal Equation", "MRI System", "Magnetic Fields and RF Coils", "Pulse Sequence", "Questions", "RF Pulses", "Signal to Noise Ratio", "Software_Resources", "Spatial Encoding", "Spectral-Spatial RF Pulses", "Spin Physics", "build_notes"], "filenames": ["Accelerated Imaging Methods.ipynb", "Artifacts.ipynb", "FOV and Resolution.ipynb", "Fast Imaging Pulse Sequences.ipynb", "Fun with RF Pulses.ipynb", "Gradient and Spin Echoes.ipynb", "Image Reconstruction.ipynb", "Introduction.md", "K-space.ipynb", "Key MRI Concepts.md", "MR Physics - Bloch Equation.ipynb", "MRI Contrast.ipynb", "MRI Math Concepts.ipynb", "MRI Notation.ipynb", "MRI Signal Equation.ipynb", "MRI System.ipynb", "Magnetic Fields and RF Coils.ipynb", "Pulse Sequence.ipynb", "Questions.md", "RF Pulses.ipynb", "Signal to Noise Ratio.ipynb", "Software_Resources.md", "Spatial Encoding.ipynb", "Spectral-Spatial RF Pulses.ipynb", "Spin Physics.ipynb", "build_notes.md"], "titles": ["Accelerated Imaging Methods", "Artifacts", "Field of View (FOV) and Resolution", "Fast Imaging Pulse Sequences", "Fun with RF Pulses?", "Gradient and Spin Echo Pulse Sequences", "Image Reconstruction", "Introduction to Principles of MRI", "K-space Encoding", "Key MRI Concepts and Equations", "Bloch Equation", "MRI Contrast", "MRI Math Concepts", "MRI Notation and Terminology", "The MRI Signal Equation and K-space", "The MRI System", "Magnetic fields in MRI", "The Pulse Sequence", "MRI Questions", "RF Pulses", "Signal to Noise Ratio (SNR)", "MRI Software Resources", "Spatial Encoding", "Spectral-Spatial RF Pulses", "Spin Physics", "&lt;no title&gt;"], "terms": {"scan": [0, 3, 7, 9, 15, 16, 18, 20], "can": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "appli": [0, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 17, 18, 19, 20, 22, 23, 24], "reduc": [0, 3, 5, 11, 18], "number": [0, 3, 10, 13, 14, 17, 23, 24], "k": [0, 1, 2, 9, 11, 18, 20, 23, 24], "space": [0, 1, 2, 9, 11, 16, 18, 20, 23], "sampl": [0, 1, 2, 6, 8, 9, 14, 18, 21, 22, 23], "also": [0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 19, 20, 22, 23, 24], "known": [0, 3, 6, 8, 11, 12, 14, 15, 16, 22, 24], "undersampl": [0, 18], "These": [0, 1, 2, 3, 4, 5, 8, 11, 14, 15, 16, 19, 22, 23, 24], "correspond": [0, 6, 8, 18, 22], "advanc": [0, 6, 11, 21], "allow": [0, 3, 11, 12, 19, 20], "The": [0, 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 16, 18, 19, 20, 22, 23, 24], "techniqu": [0, 3, 6, 8, 11], "cover": [0, 1, 8, 9, 22, 24], "here": [0, 1, 4, 7, 10, 12, 14, 17, 22, 24], "includ": [0, 1, 3, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 20, 21, 23, 24], "describ": [0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "how": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "ar": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], "form": [0, 2, 3, 6, 7, 8, 11, 14, 15, 17, 19, 22, 23, 24], "work": [0, 3, 7, 8, 9, 11, 15, 23], "understand": [0, 3, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 24], "constraint": [0, 7, 14, 20], "tradeoff": [0, 7, 14, 20], "identifi": [0, 1, 3, 5, 7, 11, 14, 17, 18, 23], "when": [0, 3, 4, 5, 9, 10, 11, 12, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24], "manipul": [0, 2, 3, 6, 7, 11, 14, 16, 17, 19, 20], "sequenc": [0, 1, 2, 6, 7, 8, 11, 13, 14, 16, 19, 20, 21, 22], "paramet": [0, 2, 6, 7, 9, 10, 11, 14, 19, 20, 23], "improv": [0, 2, 3, 6, 7, 11, 14, 18, 19, 20], "perform": [0, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22], "defin": [0, 1, 2, 6, 8, 9, 12, 14, 16, 17, 19, 20, 22, 24], "which": [0, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "modifi": [0, 1], "analyz": [0, 1, 6, 7, 10, 12, 14, 17, 19], "data": [0, 1, 3, 5, 7, 8, 9, 11, 15, 18], "an": [0, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "from": [0, 1, 3, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 19, 20, 21, 23, 24], "raw": [0, 6], "For": [0, 1, 2, 6, 7, 10, 11, 12, 14, 17, 18, 19, 20, 22, 23, 24], "help": [0, 13, 14, 17, 23, 24], "reformul": 0, "problem": [0, 18], "system": [0, 1, 6, 12, 20, 21], "us": [0, 1, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "standard": [0, 13], "mathemat": [0, 1, 16], "notat": [0, 10, 14, 16, 22], "y": [0, 4, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 22], "mathbf": 0, "e": [0, 1, 3, 6, 8, 9, 10, 11, 14, 16, 17, 18, 19, 22, 24], "x": [0, 2, 4, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 22, 23], "n": [0, 1, 2, 8, 9, 10, 11, 14, 16, 17, 19, 22, 24], "where": [0, 1, 8, 10, 11, 12, 14, 15, 16, 17, 19, 20, 22, 23, 24], "acquir": [0, 3, 5, 6, 8, 9, 11, 14, 15, 18, 20, 22], "encod": [0, 1, 3, 5, 14, 15, 16, 17], "matrix": [0, 6, 11, 22], "spatial": [0, 1, 5, 8, 12, 14, 15, 16, 17, 20], "distribut": [0, 20, 24], "transvers": [0, 3, 5, 6, 8, 9, 10, 11, 13, 14, 16, 17, 18, 22, 23, 24], "magnet": [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 18, 19, 21, 23], "g": [0, 1, 3, 6, 8, 9, 11, 12, 13, 14, 17, 18, 19, 22, 23], "nois": [0, 1, 15, 16, 18], "In": [0, 1, 2, 4, 6, 7, 8, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 24], "thi": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24], "vector": [0, 4, 10, 16, 19, 24], "exampl": [0, 2, 4, 5, 6, 14, 20, 21, 23, 24, 25], "2d": [0, 5, 6, 8, 9, 16, 18, 22, 23], "ft": [0, 12, 18], "would": [0, 1, 6, 7, 10, 15, 23, 24], "convert": [0, 6, 9, 10, 19], "left": [0, 4, 6, 10, 12, 14, 16, 22], "begin": [0, 5, 9, 10, 12, 13, 16, 20, 22, 24], "arrai": [0, 9, 12, 16, 18], "c": [0, 1, 12, 18, 24, 25], "s_1": 0, "t_1": [0, 9, 10, 11, 13, 14, 18, 20, 24], "t_2": [0, 5, 9, 10, 11, 13, 14, 18, 22, 24], "vdot": 0, "t_": [0, 1, 3, 9, 10, 17, 18, 19, 20], "nx": 0, "s_2": 0, "s_": [0, 5, 9, 11, 14], "ny": 0, "end": [0, 2, 5, 8, 9, 10, 11, 12, 13, 16, 19, 20, 22, 23, 24], "right": [0, 4, 12, 14, 22, 24], "s_m": 0, "t_n": 0, "m": [0, 5, 6, 8, 9, 10, 11, 13, 14, 16, 18, 19, 22, 24], "th": [0, 6], "tr": [0, 1, 3, 6, 9, 14, 17, 18], "x_1": 0, "y_1": 0, "x_2": 0, "x_": 0, "1": [0, 1, 2, 5, 6, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 22, 23, 24], "y_2": 0, "y_": 0, "x_i": 0, "y_i": 0, "equal": [0, 1, 2, 11, 18, 19], "locat": [0, 1, 2, 5, 6, 8, 10, 11, 12, 14, 15, 16, 19, 22, 24], "minimum": [0, 16, 17, 18], "discret": [0, 6], "transform": [0, 8, 9, 10, 11, 14, 18, 19, 22, 23], "f": [0, 1, 6, 8, 9, 11, 12, 14, 15, 18, 19, 22, 23, 24], "repres": [0, 5, 9, 11, 12, 14, 16, 18, 19, 22, 24], "our": [0, 2, 5, 6, 10, 11, 12, 14, 15, 16, 22, 24], "evalu": [0, 6, 22], "entri": [0, 1], "being": [0, 1, 10, 14, 17, 19, 20, 24], "vec": [0, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 18, 22, 24], "_i": [0, 6], "r": [0, 1, 5, 6, 9, 10, 11, 13, 14, 18, 22, 24], "_j": 0, "_": [0, 6, 9, 14, 17, 22], "i": [0, 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23], "j": [0, 24], "exp": [0, 1, 5, 8, 9, 11, 12, 14, 18, 19, 20, 22], "2": [0, 1, 2, 4, 5, 8, 9, 10, 11, 14, 16, 17, 18, 19, 20, 22, 23, 24], "pi": [0, 1, 5, 8, 9, 10, 11, 12, 14, 16, 18, 19, 20, 22, 23], "cdot": [0, 9, 11, 12, 14, 16, 18, 19, 22], "case": [0, 11, 12, 14, 19, 20], "measur": [0, 5, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 22, 24], "invers": [0, 1, 4, 6, 8, 9, 14, 18, 19, 22], "fulli": [0, 6, 8, 11, 18, 22], "well": [0, 1, 5, 6, 9, 11, 14, 16, 17, 19], "hat": [0, 11, 12, 14], "h": [0, 9, 12, 18, 23, 24], "fraction": 0, "nex": [0, 9, 18], "util": 0, "conjug": [0, 9, 18], "symmetri": [0, 9, 18], "properti": [0, 9, 10, 11, 12, 14, 18, 20, 23, 24], "state": [0, 3, 11, 18, 24], "real": [0, 8, 12, 18, 19, 22, 23, 24], "valu": [0, 10, 12, 14, 18, 19, 20, 24], "function": [0, 1, 7, 10, 11, 14, 16, 18, 19, 22, 23], "ha": [0, 5, 6, 7, 9, 10, 11, 12, 14, 16, 17, 19, 23, 24], "If": [0, 7, 10, 12, 15, 24], "satisfi": [0, 9], "mathrm": [0, 5, 6, 9, 11, 12, 16, 17, 20, 22], "mathcal": [0, 6, 9, 11, 12, 14, 18, 22, 23], "im": 0, "0": [0, 1, 2, 5, 6, 8, 9, 10, 11, 12, 14, 16, 18, 19, 20, 22, 23, 24], "object": [0, 1, 2, 6, 8, 11, 12, 14, 22], "so": [0, 5, 8, 10, 11, 14, 15, 16, 19, 20, 23, 24], "conidit": 0, "align": [0, 5, 9, 15, 16, 18, 22, 24], "across": [0, 1, 3, 5, 10, 13, 14, 15, 16, 18, 19], "entir": [0, 1, 16, 21], "With": [0, 10, 23], "strict": 0, "definit": 0, "m_": [0, 1, 5, 6, 8, 9, 10, 13, 14, 17, 18, 19, 22, 23, 24], "xy": [0, 1, 5, 6, 8, 9, 10, 13, 14, 16, 17, 19, 22, 23, 24], "mean": [0, 5, 6, 8, 10, 11, 14, 16, 18, 19, 20, 22, 24], "all": [0, 3, 5, 7, 9, 10, 12, 14, 15, 16, 17, 18, 20, 24], "along": [0, 4, 7, 10, 17, 18, 19, 24], "m_x": [0, 10, 13, 24], "practic": [0, 3, 5, 8, 12, 20, 22], "global": 0, "phase": [0, 1, 3, 4, 5, 9, 11, 14, 16, 18, 19], "offset": [0, 20], "estim": [0, 11], "relationship": [0, 2, 11, 16, 19, 20], "hold": [0, 1, 18], "long": [0, 3, 9, 11, 20], "onli": [0, 8, 9, 12, 17, 18, 19, 22, 23, 24], "half": [0, 2, 9, 18], "other": [0, 3, 4, 7, 8, 10, 14, 15, 16, 19, 20, 22, 24], "fill": 0, "time": [0, 3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 22, 23, 24], "faster": [0, 3, 18], "sourc": [0, 1, 9, 10, 11, 16, 24], "result": [0, 1, 4, 6, 10, 11, 12, 14, 15, 16, 19, 20, 22, 23, 24], "violat": [0, 23], "condit": [0, 11, 20, 24], "first": [0, 8, 10, 11, 17, 19, 22], "m_y": [0, 10, 13, 24], "sinc": [0, 1, 2, 5, 8, 11, 12, 14, 15, 16, 19, 20, 22], "correct": [0, 1, 11, 16, 18, 19, 24], "more": [0, 1, 5, 6, 7, 9, 10, 11, 14, 15, 17, 18, 19, 20, 21], "problemat": 0, "come": [0, 7, 11, 22], "rf": [0, 1, 5, 8, 11, 13, 14, 20, 22], "coil": [0, 4, 9, 17, 19, 20, 22, 24], "profil": [0, 9, 14, 19, 23], "off": [0, 1, 2, 4, 9, 11, 15, 16, 17, 22, 24], "reson": [0, 1, 4, 7, 9, 10, 11, 15, 17, 18, 22], "chemic": [0, 1, 3, 9, 11, 18, 23], "shift": [0, 1, 3, 9, 11, 18, 23], "howev": [0, 3, 5, 11, 12, 14, 19, 20, 24], "much": [0, 1, 14, 16, 17, 18, 19, 24], "addit": [0, 5, 8, 10, 11, 14, 18, 19, 20, 22], "typic": [0, 1, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23], "contain": [0, 5, 18, 19], "low": [0, 3, 11, 14, 24], "frequenc": [0, 1, 3, 4, 5, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 23], "especi": [0, 1, 20, 21], "main": [0, 1, 5, 9, 10, 11, 13, 14, 17, 18, 23, 24], "field": [0, 1, 3, 4, 5, 8, 9, 10, 11, 14, 18, 19, 20, 24], "inhomogen": [0, 1, 5, 9, 11, 14, 16, 18], "delta": [0, 1, 2, 5, 9, 11, 12, 14, 16, 19, 22, 24], "b_0": [0, 5, 9, 10, 11, 13, 14, 18, 24], "captur": [0, 2, 8, 11, 14, 15, 16, 17, 20, 22], "central": 0, "thu": [0, 12, 14, 15, 16, 18, 19, 22, 24], "slightli": [0, 5, 9, 17, 19, 24], "than": [0, 9, 11, 16, 18], "special": [0, 4], "algorithm": [0, 6, 12, 23], "project": 0, "onto": [0, 14], "convex": 0, "set": [0, 7, 11, 12], "poc": 0, "homodyn": 0, "detect": [0, 9, 15, 16, 18, 24], "we": [0, 1, 2, 5, 6, 8, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 24], "need": [0, 9, 12, 15, 18, 20, 22, 24, 25], "consid": [0, 10, 11, 14, 19, 20, 24], "sensit": [0, 1, 3, 9, 15, 18, 22], "_q": 0, "each": [0, 3, 6, 11, 12, 14, 16, 17, 20], "sub": [0, 13, 23], "oper": [0, 12, 14, 18], "s": [0, 1, 5, 7, 9, 10, 11, 13, 14, 16, 18, 20, 22, 23, 24], "y_q": 0, "n_q": 0, "c_q": 0, "diagon": 0, "diagnoal": 0, "whether": [0, 1, 9], "expect": [0, 10, 11, 14, 17, 18, 20], "grid": [0, 6, 8, 22], "wa": [0, 3, 5, 7], "It": [0, 3, 5, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 22, 24], "conveni": [0, 24], "point": [0, 14, 20, 24], "return": [0, 10, 15, 24], "origin": [0, 1, 3, 12, 14, 16, 24], "creat": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 15, 17, 18, 19, 22, 23, 24], "augment": 0, "matric": [0, 11, 14], "concaten": 0, "element": [0, 9, 14], "dimens": [0, 6, 8, 11, 12, 14, 20, 22, 23], "ldot": [0, 8, 9, 22], "y_n": 0, "_1": [0, 11], "_2": [0, 11], "_n": 0, "n_1": 0, "n_2": 0, "n_n": 0, "ex": [0, 19], "some": [0, 1, 4, 7, 8, 14, 16, 17, 19, 20, 22], "simul": [0, 4, 7, 8, 11, 19, 21, 22], "espirit": 0, "nlinv": 0, "singl": [0, 1, 3, 9, 11, 14, 16, 17, 18, 19, 22], "underli": 0, "solv": [0, 14], "optim": [0, 9, 11, 20], "popular": [0, 3, 5, 7, 21], "arg": 0, "min_": 0, "frac": [0, 1, 2, 5, 8, 9, 10, 11, 12, 18, 19, 20, 22, 24], "2_2": 0, "directli": [0, 11, 18], "pseudo": [0, 9, 18], "calcul": [0, 10, 18], "pattern": [0, 2, 8, 9, 11, 17, 18, 19, 22], "regular": 0, "consist": [0, 8, 11, 15, 22, 23], "skip": [0, 1, 9], "line": [0, 1, 2, 3, 6, 7, 8, 9, 10, 14, 16, 17, 18, 22, 23], "assum": [0, 9, 14], "combin": [0, 14, 23], "inlcud": 0, "auto": 0, "smash": 0, "grappa": 0, "spirit": 0, "calibr": [0, 18], "kernel": [0, 14], "comput": [0, 12], "itself": 0, "follow": [0, 5, 6, 7, 8, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22], "lambda": 0, "tune": [0, 16], "ident": [0, 19], "simultan": [0, 9, 18], "enforc": 0, "term": [0, 10, 11, 14, 18], "self": 0, "sescond": 0, "either": [0, 14, 18, 19, 20], "iter": 0, "while": [0, 1, 5, 10, 11, 14, 15, 19, 20, 23], "full": [0, 2, 3, 7, 10, 13, 14, 18, 24], "center": [0, 3, 6, 8, 9, 11, 14, 16, 17, 18, 19, 22], "There": [0, 1, 5, 10, 19, 20], "penalti": 0, "vari": [0, 8, 10, 11, 13, 14, 15, 16, 19, 20, 22, 23, 24], "sever": [0, 5], "depend": [0, 1, 5, 8, 10, 11, 14, 16, 18, 22, 24], "variat": [0, 4, 5, 8, 9, 15, 21, 22], "direct": [0, 1, 4, 8, 9, 10, 14, 16, 18, 22, 23, 24], "lead": [0, 1, 3, 5, 9, 11, 12, 14, 19, 20, 22], "lower": [0, 11, 20], "convers": 0, "less": [0, 7, 9, 19, 24], "ill": 0, "higher": [0, 1, 11, 19, 20, 24], "penatli": 0, "region": [0, 1, 16], "littl": 0, "differ": [0, 1, 5, 6, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 22, 24], "betweeen": 0, "bodi": [0, 11, 16, 18, 19, 24], "tend": 0, "have": [0, 1, 4, 9, 10, 11, 16, 18, 19, 20, 22, 24], "larger": [0, 1, 14, 16, 18], "character": [0, 1, 5, 8, 12, 14, 18, 19, 22], "factor": [0, 14, 18, 20], "geq": 0, "loss": [0, 1, 14, 18, 20], "load": [0, 1, 5, 6, 10, 11, 14, 15, 19, 20, 23, 24], "geometri": 0, "appyl": 0, "total": [0, 9, 18, 19, 20, 24], "readout": [0, 3, 6, 8, 14, 17, 18, 20, 22], "sqrt": [0, 8, 9, 11, 12, 16, 18, 19, 20, 22], "snr_": [0, 18, 20], "appear": [0, 1, 9, 11, 19], "alias": [0, 18], "sometim": [0, 10, 17], "complet": [0, 5, 7, 8, 10, 18, 22], "remov": [0, 5, 10, 11, 14, 19, 20, 23], "like": [0, 7, 15, 19], "mismatch": 0, "between": [0, 3, 5, 9, 11, 14, 16, 17, 18, 19, 24], "cs": [0, 11, 14], "theori": [0, 12], "sai": [0, 16], "domain": [0, 8, 9, 12, 18, 22], "subset": 0, "word": [0, 4, 15, 19, 22], "further": [0, 14], "acquisit": [0, 3, 5, 6, 8, 9, 11, 15, 18, 22], "specif": [0, 1, 3, 5, 10, 14, 15, 22, 24], "ell_1": 0, "norm": 0, "sum_": [0, 12], "promot": 0, "sparsiti": [0, 9, 11], "solut": [0, 10, 14, 19], "lambda_": 0, "wx": 0, "multipli": [0, 11, 12, 14], "must": [0, 17, 18, 24, 25], "match": [0, 18, 20], "spars": [0, 9, 18], "through": [0, 14, 16, 17, 19, 20, 23], "sparsifi": 0, "w": [0, 14, 18], "chosen": [0, 11], "balanc": [0, 3, 18], "random": [0, 1, 6, 9, 18], "illustrat": 0, "diagram": [0, 5, 18], "below": [0, 1, 4, 5, 6, 10, 11, 12, 14, 16, 17, 19, 23, 24], "procedur": 0, "caption": 0, "figur": [0, 1, 2, 8, 10, 11, 12, 14, 19, 20, 22, 23, 24], "http": [0, 1, 4, 5, 12, 13, 24], "doi": 0, "org": [0, 1, 12, 13], "10": [0, 7, 8, 10, 11, 14, 16, 18, 22, 23], "1109": 0, "msp": 0, "2007": 0, "914728": 0, "heurist": 0, "A": [0, 1, 3, 5, 10, 12, 16, 17, 18, 19, 23, 24], "signal": [0, 1, 3, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 18, 19, 21, 23, 24], "8": [0, 2, 8, 10, 11, 12, 16, 19, 22, 23, 24], "fold": [0, 1], "its": [0, 5, 7, 10, 11, 14, 18, 24], "d": [0, 5, 8, 9, 10, 14, 19, 20, 22], "b": [0, 9, 10, 12, 13, 15, 16, 24], "equispac": 0, "prevent": 0, "recoveri": [0, 9, 18], "incoher": [0, 1], "interfer": [0, 1, 16], "strong": [0, 11, 20, 24], "compon": [0, 1, 7, 14, 16, 18, 24], "stick": 0, "abov": [0, 7, 8, 11, 12, 14, 16, 18, 19, 20, 22, 23, 24], "level": [0, 1, 9, 11], "recov": [0, 11, 24], "threshold": 0, "subtract": [0, 15, 16], "enabl": [0, 15, 18], "weaker": 0, "tv": 0, "tgv": 0, "wavelet": 0, "variabl": [0, 12], "densiti": [0, 9, 18, 20, 24], "preferenti": [0, 15, 18, 24], "difficult": 0, "thei": [0, 1, 3, 4, 7, 11, 15, 16, 17, 18, 19, 24], "inher": [0, 9], "denois": 0, "constrain": 0, "appar": [0, 22], "significantli": 0, "choic": [0, 11, 20], "most": [0, 3, 5, 7, 8, 9, 10, 11, 12, 14, 16, 17, 19, 22, 23, 24], "common": [0, 3, 8, 9, 16, 22, 23], "overfit": 0, "over": [0, 6, 8, 10, 13, 14, 16, 17, 20, 22], "smooth": 0, "unnatur": 0, "block": [0, 5, 17], "conceptu": 0, "train": [0, 3, 9, 18], "incorpor": [0, 12, 14, 20], "inform": [0, 1, 10, 11, 14, 17, 18, 20, 23, 24], "world": 0, "relev": [0, 12], "been": [0, 6, 11], "shown": [0, 5, 6, 10, 14, 16, 17, 19, 23, 24], "support": [0, 3, 9], "what": [0, 1, 2, 5, 7, 8, 10, 14, 15, 16, 17, 18, 24], "within": [0, 3, 9, 11, 17, 18, 19, 20, 22], "often": [0, 5, 11, 12, 14, 17, 20], "least": [0, 16, 18], "squar": [0, 20], "reg": 0, "implicitli": 0, "implement": [0, 19, 20], "via": [0, 7], "machin": 0, "attempt": [0, 7], "straightforward": 0, "approach": [0, 20], "cnn": 0, "invert": [0, 5], "after": [0, 3, 5, 8, 9, 10, 11, 15, 16, 17, 18, 22, 24], "g_": [0, 8, 9, 18, 19, 22], "dnn": 0, "neural": [0, 9], "network": [0, 9, 18, 21], "mani": [0, 1, 7, 11, 12, 14, 16, 17, 18, 21, 24], "weight": [0, 1, 3, 5, 9, 18, 20, 23], "prior": [0, 18, 22], "abl": [0, 24], "call": [0, 3, 4, 5, 8, 10, 11, 16, 19, 23, 24], "un": 0, "roll": 0, "becom": [0, 3, 14, 19, 22], "better": 0, "compact": 0, "design": [0, 7, 10, 15, 16, 20, 21], "mimic": 0, "classic": 0, "seri": 0, "cascad": 0, "modl": 0, "varnet": 0, "regularl": 0, "architectur": [0, 18], "gradient": [0, 1, 2, 6, 8, 9, 11, 13, 14, 18, 19, 20, 23], "updat": [0, 7, 10, 14, 23, 24], "descent": 0, "unet": [0, 18], "arxiv": 0, "ab": [0, 1, 2, 11, 12, 14, 19, 23], "2004": 0, "06688": 0, "e2": 0, "vn": 0, "take": [0, 4, 8, 11, 19, 20, 22], "under": [0, 7, 10, 20, 24], "input": [0, 12], "ift": 0, "rss": 0, "bottom": [0, 4, 10, 16], "dc": 0, "modul": [0, 1, 14, 19, 20, 22], "bring": [0, 15], "intermedi": [0, 11, 19], "closer": [0, 24], "refin": 0, "map": [0, 1, 8, 9, 18, 21, 22], "multi": [0, 9, 11, 18], "one": [0, 8, 10, 12, 14, 18, 20, 22, 23, 24], "u": [0, 25], "net": [0, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 17, 18, 19, 21, 22, 24], "back": [0, 4, 10, 11, 14, 19, 23, 24], "sme": 0, "step": [0, 1, 8, 9, 18, 22, 23, 24], "_w": 0, "structur": [0, 11, 13, 24], "overal": [0, 5, 7, 11, 14, 17, 20, 23], "similar": [0, 11, 12, 14], "both": [0, 3, 5, 8, 10, 17, 22, 23, 24], "unrol": [0, 18], "lot": [0, 7], "4": [0, 1, 2, 7, 11, 12, 15, 16, 19, 20, 23], "radiolog": 0, "applic": [0, 7, 24], "question": [0, 15], "answer": [0, 15, 18], "qualiti": [0, 14, 20], "supervis": 0, "realist": 0, "modif": [0, 18, 20], "exist": 0, "increas": [0, 1, 3, 16, 18, 19, 20, 24], "size": [0, 1, 2, 5, 11, 12, 18, 20], "fastmri": 0, "provid": [0, 1, 8, 9, 11, 14, 16, 19, 20, 22, 23], "thousand": 0, "high": [0, 1, 3, 9, 14, 16, 17], "med": 0, "nyu": 0, "edu": 0, "48550": 0, "1811": 0, "08839": 0, "resnet": 0, "possibl": [0, 16, 18, 20], "gpu": 0, "essenti": 0, "send": 0, "forward": 0, "compar": [0, 13, 18, 19, 20, 24], "output": [0, 12], "propag": 0, "choos": [0, 11, 20, 24], "l1": 0, "l2": 0, "batch": 0, "rate": [0, 1, 5, 10, 11, 13, 14, 17, 20, 23, 24], "etc": [0, 20], "challeng": [0, 7], "retain": 0, "textur": 0, "featur": [0, 10, 19, 21], "anatomi": [0, 16, 18], "might": 0, "eras": 0, "hallucin": 0, "although": [0, 4, 24], "physic": [0, 11, 20], "assur": 0, "recent": 0, "comprehens": [0, 1], "thes": 0, "reccommend": 0, "hammernik": 0, "k\u00fcstner": 0, "t": [0, 5, 6, 8, 9, 10, 12, 13, 14, 18, 19, 22, 23, 24], "yaman": 0, "huang": 0, "z": [0, 1, 4, 9, 10, 11, 13, 16, 17, 18, 19, 20, 23, 24], "rueckert": 0, "knoll": 0, "ak\u00e7akaya": 0, "driven": [0, 9], "medic": 0, "ieee": 0, "process": [0, 5, 7, 10, 12, 16, 21, 24], "mag": 0, "2023": [0, 7], "jan": 0, "40": [0, 11], "98": 0, "114": 0, "2022": 0, "3215288": 0, "epub": 0, "pmid": 0, "37304755": 0, "pmcid": 0, "pmc10249732": 0, "pdf": 0, "2203": 0, "12215": 0, "setup": [1, 2, 5, 6, 10, 11, 14, 15, 16, 19, 20, 23, 24, 25], "mri": [1, 2, 3, 5, 8, 10, 17, 19, 20, 23, 24], "educ": [1, 2, 5, 6, 10, 11, 14, 15, 16, 19, 20, 21, 23, 24], "resourc": [1, 2, 5, 6, 10, 11, 13, 14, 15, 16, 19, 20, 23, 24], "path": [1, 2, 5, 6, 10, 11, 14, 15, 16, 19, 20, 23, 24], "requir": [1, 2, 3, 4, 5, 6, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 23, 24], "cd": [1, 2, 5, 6, 10, 11, 14, 15, 16, 19, 20, 23, 24], "startup": [1, 2, 5, 6, 10, 11, 14, 15, 16, 19, 20, 23, 24], "notebook": [1, 21], "variou": [1, 3, 5, 7, 11, 16, 17, 19], "wikipedia": [1, 12], "en": [1, 12], "wiki": [1, 12], "mri_artifact": 1, "veri": [1, 6, 8, 10, 11, 14, 15, 17, 19, 20, 22], "mitig": [1, 3, 5, 7, 14, 23], "them": [1, 3, 5, 7, 11, 14, 15, 16, 23, 24], "occur": [1, 10, 11, 14, 15, 18, 20, 24], "understood": 1, "perspect": 1, "particular": [1, 17], "equat": [1, 16, 18, 19, 22], "section": [1, 5, 8, 11, 22], "gener": [1, 3, 5, 8, 11, 13, 14, 18, 21, 22], "categor": 1, "tabl": [1, 16], "name": [1, 5, 8, 10, 19, 22], "do": [1, 10, 11, 14, 15], "fov": [1, 9, 11, 15, 16], "too": 1, "small": [1, 11, 15, 16, 19, 21, 24], "parallel": [1, 8, 9, 18, 22], "fail": 1, "swap": [1, 12], "pe": [1, 8, 9, 22], "fe": [1, 18], "reacquir": 1, "gibb": [1, 14, 18], "ring": [1, 12, 14, 18, 19], "truncat": [1, 18], "due": [1, 5, 9, 11, 14, 15, 18, 20, 22], "fourier": [1, 8, 9, 11, 14, 18, 19, 22, 23], "edg": [1, 12, 14, 18], "rippl": [1, 19], "sharp": [1, 12, 19], "filter": [1, 14, 18, 23], "boundari": 1, "partial": [1, 6, 9, 18], "volum": [1, 9, 16, 22], "opposit": 1, "voxel": [1, 2, 3, 5, 9, 13, 18], "artifici": 1, "dark": [1, 18], "tissu": [1, 11, 14, 18, 19, 24], "fat": [1, 9, 14, 18, 23], "suppres": 1, "water": [1, 9, 14, 18, 23, 24], "dure": [1, 3, 5, 6, 7, 8, 9, 11, 15, 16, 17, 18, 19, 20, 22, 23], "copi": 1, "ghost": [1, 3, 18], "chang": [1, 2, 3, 4, 5, 9, 10, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "breath": 1, "gate": 1, "trigger": 1, "compens": 1, "suscept": [1, 3, 5, 9, 11, 14, 18, 21], "bandwidth": [1, 9, 18], "shim": 1, "suppress": [1, 9, 18, 23], "2dft": [1, 18], "epi": [1, 9, 14, 18, 23], "slice": [1, 9, 17, 18, 23], "3d": [1, 6, 8, 9, 22, 24], "suscpet": 1, "implant": 1, "air": 1, "spin": [1, 4, 10, 11, 13, 14, 15, 16, 18, 19, 20], "echo": [1, 4, 8, 9, 11, 13, 14, 17, 18, 20, 22, 23], "dielectr": 1, "shade": 1, "propog": 1, "unevenli": 1, "b1": [1, 4], "particularli": [1, 3, 14, 23], "larg": [1, 3, 5, 9, 15, 16, 19, 24], "b0": [1, 10, 16, 18], "insensit": [1, 4], "puls": [1, 7, 8, 11, 13, 14, 20, 21, 22], "adiabat": 1, "bia": 1, "zipper": 1, "unwant": [1, 4], "noisi": 1, "top": [1, 10, 24], "shield": 1, "close": [1, 10, 14, 16, 23, 24], "door": 1, "check": [1, 4], "hardwar": [1, 15], "room": 1, "light": [1, 18], "At": [1, 18], "non": [1, 8, 10, 19, 22, 24], "linear": [1, 6, 12, 14, 16, 19, 20, 22], "awai": [1, 10, 11, 16, 24], "isocent": 1, "subject": [1, 5, 10, 14, 15, 24], "warp": 1, "spike": 1, "intermitt": 1, "loos": 1, "connect": 1, "broken": [1, 5], "reli": [1, 3, 18], "unknown": 1, "disort": 1, "delta_": 1, "rbw": [1, 18], "fov_": [1, 2], "receiv": [1, 9, 13, 14, 15, 17, 18, 22], "view": [1, 8, 10, 11, 15, 18, 20, 22], "accumul": [1, 5, 6, 8, 14, 22], "esp": [1, 3, 9], "adjac": [1, 11], "n_": [1, 8, 9, 18, 22, 24], "To": [1, 5, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 24], "bw_": [1, 9, 18, 19], "ani": [1, 5, 7, 8, 10, 11, 14, 18, 20, 22, 24], "interleav": [1, 9], "without": [1, 10, 14], "acceler": [1, 3], "shot": [1, 3], "final": [1, 10, 14, 16], "select": [1, 9, 10, 11, 17, 18, 21, 23], "ss": [1, 9, 19], "inconsist": 1, "period": [1, 11, 19], "heart": 1, "beat": 1, "pulsatil": 1, "distinct": [1, 20], "sequenti": [1, 3, 18], "predict": [1, 9], "interv": 1, "60": [1, 11, 19], "per": [1, 9, 11], "minut": [1, 7], "irregular": 1, "arrhytthmia": 1, "cough": 1, "bulk": 1, "diffus": [1, 3, 14, 20, 21, 23], "datanam": 1, "se_t1_sag_data": 1, "kdata": [1, 2], "im_origin": 1, "ifft2c": [1, 2, 11, 14], "subplot": [1, 2, 8, 14, 16, 19, 20, 22, 23], "121": [1, 8, 14, 20, 22, 23], "imagesc": [1, 2, 11, 16, 23], "log": [1, 2], "max": [1, 2, 9, 20, 23], "colormap": [1, 2, 11, 16, 23], "grai": [1, 2, 11, 16, 23], "axi": [1, 2, 3, 4, 10, 11, 16, 18, 24], "tight": [1, 2, 11, 16], "122": [1, 8, 14, 20, 22, 23], "warn": [1, 10, 14, 23, 24], "user": 1, "plarson": 1, "document": 1, "github": [1, 7], "mat": 1, "found": [1, 11], "search": 1, "n_undersamp": 1, "data_undersamp": 1, "zero": [1, 8, 10, 11, 19, 20, 22, 23, 24], "iundersamp": 1, "round": [1, 16, 23], "im_undersamp": 1, "spike_loc": 1, "6": [1, 8, 10, 12, 19, 20, 22, 23, 24], "53": 1, "data_spik": 1, "5": [1, 2, 8, 9, 10, 12, 14, 15, 16, 19, 20, 22, 23, 24], "im_spik": 1, "rect": [1, 12], "32": [1, 12, 14], "kx": [1, 2, 8, 11, 12, 14, 18, 22], "n_rect": [1, 2], "rect_ring": 1, "221": [1, 2, 19, 23], "222": [1, 2, 19], "ylabel": [1, 8, 10, 11, 14, 16, 19, 20, 22, 23, 24], "kdata_window": 1, "ham": [1, 19], "rect_window": 1, "223": [1, 19, 23], "224": [1, 19], "window": [1, 10, 14, 19, 23, 24, 25], "relative_rf_frequ": 1, "ph_int": 1, "rand": 1, "rfint": 1, "data_rfint": 1, "repmat": [1, 14, 19], "im_rfint": 1, "amplitud": [1, 4, 8, 9, 11, 14, 16, 17, 18, 19, 22, 24], "3": [1, 2, 8, 9, 10, 15, 16, 19, 20, 22, 23, 24], "randn": 1, "imag": [2, 5, 7, 10, 12, 14, 15, 16, 17, 19, 20, 23, 24], "fundament": [2, 11, 24], "determin": [2, 12, 14, 15, 16, 17, 18, 19, 22, 23], "cell": [2, 8, 16, 22], "syntaxerror": [2, 8, 16, 22], "invalid": [2, 8, 16, 22], "syntax": [2, 8, 16, 22], "simpl": [2, 20], "base": [2, 6, 7, 9, 11, 12, 14, 16, 18, 19, 20, 22], "k_x": [2, 8, 12, 14, 18, 22], "rectangular": [2, 19], "demonstr": [2, 23], "256": [2, 11], "rect_recon": 2, "titl": [2, 8, 10, 11, 12, 14, 16, 19, 20, 22, 23, 24], "kdata2": 2, "rect_recon2": 2, "doubl": 2, "kdata3": 2, "rect_recon3": 2, "tripl": 2, "One": [2, 4, 10, 16, 20, 24], "third": 2, "maximum": [2, 8, 9, 15, 16, 18, 20, 22], "extent": [2, 16], "k_": [2, 9], "delta_x": [2, 18, 20], "symmetr": 2, "width": [2, 12], "w_k": 2, "kdata4": 2, "rect_recon4": 2, "4x": 2, "kdata8": 2, "7": [2, 16], "16": [2, 12], "9": [2, 10, 24], "rect_recon8": 2, "8x": 2, "modern": 3, "heavili": 3, "primarili": [3, 7, 9, 17], "method": [3, 5, 6, 8, 11, 17, 20, 21, 22], "acronym": [3, 5, 7], "contrast": [3, 5, 7, 10, 14, 17, 19, 24], "artifact": [3, 5, 7, 11, 12, 14, 16, 21, 23], "distort": [3, 9, 16, 18, 21], "t2": [3, 9, 10, 14, 18, 20, 21, 24], "blur": [3, 14, 18], "band": [3, 18], "bssfp": [3, 18], "refocus": [3, 4, 9, 11, 18, 19, 23], "exict": 3, "rapid": [3, 15], "relax": [3, 7, 9, 11, 13, 17, 18, 20, 22], "enhanc": [3, 14], "scanner": [3, 17, 18, 24], "ge": [3, 11, 18], "healthcar": 3, "turbo": 3, "siemen": 3, "healthin": 3, "tfe": [3, 8, 22], "philip": 3, "clinic": [3, 18], "becaus": [3, 5, 10, 15, 18, 24], "highli": 3, "snr": [3, 9, 14], "effici": [3, 11, 18], "effect": [3, 4, 8, 9, 11, 12, 14, 20], "pd": [3, 9], "length": [3, 8, 9, 10, 11, 16, 19, 20, 22, 23, 24], "etl": [3, 9], "repetit": [3, 11, 17, 18], "te": [3, 5, 9, 14, 17, 18, 20], "te_": [3, 9, 11], "eff": [3, 9], "closest": [3, 9, 16], "pro": 3, "con": 3, "sar": [3, 9, 18, 19], "repeat": [3, 5, 8, 9, 11, 15, 17, 18, 22, 23, 24], "commonli": [3, 11, 12, 15, 18], "fmri": [3, 23], "extrem": [3, 12, 20, 24], "displac": [3, 18, 23], "fidel": 3, "nyquist": [3, 18], "basic": [3, 4, 11, 12, 17, 21], "befor": [3, 8, 11, 18, 19, 22], "next": [3, 8, 18, 22], "unbalanc": 3, "dephas": [3, 5, 8, 9, 11, 18, 22], "elimin": [3, 5, 9, 11, 18, 23], "truli": 3, "rotat": [3, 4, 8, 9, 14, 16, 17, 18, 19, 22, 24], "everi": [3, 5, 11, 16, 17, 18, 20], "chanc": 3, "previou": 3, "coher": 3, "excit": [3, 5, 8, 9, 11, 13, 15, 18, 22, 23], "scheme": [3, 11], "quadrat": 3, "increment": [3, 8, 22], "spgr": 3, "angl": [3, 4, 5, 9, 16, 17, 18, 20, 24], "flash": 3, "aim": [3, 19, 23], "pure": [3, 5], "t1": [3, 9, 10, 18, 20, 21, 24], "recal": [3, 5, 6], "steadi": [3, 11, 18], "grass": 3, "precess": [3, 5, 9, 14, 16, 18, 22], "fisp": 3, "residu": [3, 14], "refouc": 3, "free": [3, 18], "ssfp": [3, 14], "revers": [3, 5, 12, 22], "psif": 3, "refocu": [3, 5, 18], "later": [3, 11, 14, 16, 17, 24], "truefisp": 3, "No": [3, 5], "preserv": 3, "ye": 4, "you": [4, 5, 7, 10, 11, 13, 24], "heard": 4, "me": 4, "mayb": 4, "type": [4, 5, 7, 8, 11, 13, 14, 15, 17, 18, 19, 20, 22], "person": 4, "think": 4, "out": [4, 5, 6, 8, 9, 11, 13, 14, 18, 20, 22], "interest": [4, 16, 20], "movi": [4, 8, 22], "spinbench": [4, 7], "heartvista": 4, "ai": 4, "class": [4, 5, 11], "b_1": [4, 9, 13, 19, 23, 24], "inhomongen": 4, "similarli": [4, 12, 20], "even": 4, "transmit": [4, 9, 13, 15, 18], "mostli": 4, "180": [4, 5, 10, 11, 18, 19, 20], "degre": [4, 5, 10, 18, 19, 20], "flip": [4, 5, 9, 16, 17, 18, 20, 23], "purpos": [4, 15, 16, 17, 19, 21], "show": [4, 6, 8, 10, 11, 12, 14, 16, 17, 19, 22], "two": [4, 5, 20, 23, 24], "sweep": 4, "again": [4, 10, 14, 24], "second": [4, 11, 17], "yellow": 4, "white": [4, 11], "rang": [4, 7, 11, 15, 16, 18, 19, 21], "around": [4, 10, 11, 15, 16, 17, 19, 24], "larmor": [4, 10, 11, 16, 17, 18, 19, 24], "plot": [4, 8, 10, 11, 12, 14, 16, 19, 20, 22, 23, 24], "corner": 4, "continu": [4, 12, 24], "constant": [4, 5, 8, 9, 11, 18, 19, 22, 24], "hard": [4, 5, 10, 18], "frequneci": [4, 14, 22], "broad": [5, 7], "simpler": 5, "undesir": [5, 11], "build": [5, 14, 19, 21, 25], "g_x": [5, 8, 13, 18, 22], "cancel": 5, "anoth": [5, 11, 19, 24], "And": [5, 14, 16, 20, 24], "simplifi": [5, 10, 14, 22, 24], "exhibit": 5, "explain": [5, 7, 10], "propto": [5, 9, 11, 19, 20], "m_0": [5, 9, 10, 11, 13, 18, 20, 24], "ideal": [5, 11, 12, 17], "uniform": 5, "absens": [5, 24], "unavoid": 5, "refer": [5, 8, 10, 15, 19, 22, 24], "f_r": [5, 11, 14], "bar": [5, 8, 9, 10, 11, 13, 14, 15, 16, 19, 22, 24], "gamma": [5, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 22, 23, 24], "imperfect": [5, 14], "decai": [5, 11, 18, 24], "smallest": 5, "sum": [5, 9, 14, 19, 22, 23, 24], "int_": [5, 12, 20, 22], "approx": [5, 11, 16, 22, 24], "note": [5, 6, 7, 8, 11, 12, 14, 16, 17, 18, 19, 20, 22], "reconstruct": [5, 8, 9, 11, 12, 14, 21, 22], "mechan": [5, 11], "de": 5, "averag": [5, 20], "magnitud": [5, 16, 18, 19], "illustr": [5, 6, 8, 10, 11, 12, 19, 21, 22, 24], "t2star_spinecho_illustr": 5, "80": [5, 10, 11, 24], "ms": [5, 10, 11, 14, 16, 19, 20, 23], "mild": 5, "approxim": [5, 9, 11, 18, 19, 20, 23], "up": [5, 7, 10, 11, 14, 16, 18, 19, 24], "separ": [5, 9, 11, 14, 15, 16, 18, 23, 24], "leq": [5, 11], "easili": [5, 20, 23], "doe": [5, 9, 14, 18, 20, 25], "make": [5, 15], "revert": 5, "try": [5, 10, 12], "visit": 5, "drcmr": [5, 24], "dk": [5, 24], "blochsimul": 5, "scene": [5, 10], "90x": [5, 10], "180y": 5, "happen": [5, 18, 19], "180x": 5, "Is": 5, "still": [5, 12], "multipl": [5, 9, 11, 12, 17, 18, 19], "order": [5, 6, 11, 22, 23, 24], "give": [5, 15, 16, 18], "collect": [6, 18], "cartesian": [6, 14], "done": [6, 11, 14, 17, 20, 23, 24], "anticip": 6, "formul": [6, 9, 12, 14, 22, 23, 24], "introduc": [6, 11, 17, 19, 22, 24], "proport": [6, 8, 9, 11, 16, 18, 19, 20, 22, 24], "s_i": 6, "denot": [6, 12, 14, 16], "subscript": 6, "trajectori": [6, 9, 14, 23], "raster": [6, 8, 22], "fashion": [6, 17], "knowledg": [6, 14], "mr": [6, 11, 13, 16, 20, 22, 23, 24], "store": [6, 18, 22], "onc": [6, 7, 8, 11, 14, 20, 22, 24], "simpli": [6, 12, 14, 15, 16, 24], "fast": [6, 12, 14], "fft": [6, 12, 19], "anim": [6, 7, 10, 19], "short": [7, 9, 11, 19], "book": [7, 13, 25], "associ": [7, 10, 18, 19], "larsonlab": 7, "repositori": 7, "helper": [7, 11], "built": 7, "about": [7, 17, 19, 24], "decad": 7, "teach": 7, "1st": 7, "year": 7, "graduat": 7, "student": 7, "background": [7, 16], "natur": [7, 11], "scienc": 7, "engin": 7, "undergo": 7, "fall": 7, "quarter": 7, "promin": 7, "role": 7, "my": [7, 21], "upon": 7, "should": [7, 10, 16, 19, 20, 23, 24], "achiev": [7, 10, 11, 15, 18, 19, 24], "fundmanet": [7, 15, 16], "why": [7, 9, 15, 16, 22], "necessari": [7, 12, 15, 16, 17, 19], "concept": [7, 10, 14, 18, 21, 22, 24], "polar": [7, 9, 10, 13, 15, 16, 18, 22], "jump": 7, "pretti": 7, "quickli": [7, 19], "quick": 7, "overview": 7, "access": 7, "playlist": 7, "record": [7, 17], "goe": [7, 19], "avail": [7, 9, 10, 19, 21, 24], "git": 7, "icon": 7, "recommend": [7, 10, 14, 23, 24], "clone": 7, "desktop": 7, "wai": [7, 8, 11, 16, 17, 18, 22], "pull": 7, "made": [7, 10, 14, 23, 24], "greatli": [7, 10, 14], "influenc": [7, 10, 14, 20], "great": 7, "want": 7, "front": 7, "dwight": 7, "nishimura": 7, "text": 7, "borrow": 7, "materi": [7, 11, 15], "own": [7, 14], "bill": 7, "tool": [7, 12, 17, 21], "miki": 7, "lustig": 7, "danish": 7, "research": 7, "centr": 7, "bloch": [7, 14, 18, 19, 24], "By": [8, 11, 16, 22], "far": [8, 16, 22], "fact": [8, 22], "regularli": [8, 22], "turn": [8, 9, 10, 16, 17, 18, 22, 24], "read": [8, 17, 18, 20, 22], "present": [8, 10, 11, 12, 16, 22], "given": [8, 9, 11, 18, 19, 22, 24], "convent": [8, 16, 22, 24], "xr": [8, 9, 18, 22], "therefor": [8, 11, 15, 20, 22, 24], "posit": [8, 9, 16, 18, 19, 22, 23], "alon": [8, 20, 22], "1d": [8, 22], "mxy": [8, 18, 22], "ones": [8, 10, 11, 12, 19, 22, 23], "meshgrid": [8, 11, 14, 19, 22], "splot": [8, 22], "kfe": [8, 22], "dt": [8, 10, 11, 14, 19, 22, 23], "42": [8, 10, 14, 19, 22, 23, 24], "58": [8, 10, 14, 19, 22, 23], "linspac": [8, 10, 11, 12, 16, 19, 20, 22, 23, 24], "phase_x": [8, 22], "mxy_f": [8, 22, 23], "05": [8, 16, 22], "quiver": [8, 16, 22], "xlabel": [8, 10, 11, 12, 14, 16, 19, 20, 22, 23, 24], "xlim": [8, 19, 22], "ylim": [8, 20, 22], "drawnow": [8, 22], "2nd": [8, 11, 22], "option": [8, 10, 22], "3rd": [8, 22], "phi": [8, 9, 12, 22], "yp": [8, 16, 22], "yi": [8, 9, 22], "t_y": [8, 9, 22], "strength": [8, 9, 10, 16, 18, 20, 22], "durat": [8, 10, 14, 18, 19, 20, 22], "equival": [8, 19, 20, 22], "kpe": [8, 22], "tpe": [8, 22], "ip": [8, 22], "phase_i": [8, 22], "mxy_p": [8, 22], "g_y": [8, 13, 18, 22], "int2str": [8, 11, 14, 19, 20, 22], "instead": [8, 10, 14, 22, 23, 24], "visual": [8, 10, 19, 22, 24], "see": [8, 9, 10, 11, 14, 15, 17, 20, 22, 24], "spatial_encoding_mxy_illustr": [8, 22], "code": [8, 10, 21, 22, 23], "int_0": [8, 9, 14, 19, 20, 22], "tau": [8, 9, 12, 14, 18, 19, 20, 22], "alwai": [8, 11, 15, 16, 18, 22, 24], "start": [8, 10, 12, 14, 15, 18, 22, 24], "initi": [8, 11, 14, 22], "neg": [8, 22], "experi": [8, 10, 11, 14, 16, 17, 20, 22, 24], "radial": [8, 14, 22], "spiral": [8, 14, 22], "planar": [8, 14, 18, 22, 23], "blade": [8, 22], "ky": [8, 11, 14, 22], "linewidth": [8, 12, 22], "k_y": [8, 12, 14, 18, 22], "kx_ep": [8, 22], "ky_ep": [8, 22], "k_theta": [8, 22], "k_radial": [8, 22], "201": [8, 22, 23], "nturn": [8, 22], "k_spiral": [8, 22], "kz": [8, 22], "plot3": [8, 22, 23], "reshap": [8, 14, 22], "zlim": [8, 22], "zlabel": [8, 11, 22], "k_z": [8, 22, 23], "n_radial": [8, 22], "co": [8, 9, 10, 11, 12, 16, 18, 20, 22], "asin": [8, 22], "sin": [8, 9, 10, 11, 12, 16, 20, 22], "math": [9, 10], "electr": [9, 15, 16], "nuclear": [9, 15, 16], "equilibrium": [9, 10, 11, 13, 15, 16], "i_z": [9, 24], "bmatrix": [9, 10, 13, 16, 24], "static": [9, 18], "m_z": [9, 10, 11, 13, 18, 19, 24], "radiofrequ": 9, "homogen": [9, 15, 16], "proton": [9, 18, 20, 23, 24], "spoil": [9, 18, 20], "gre": [9, 18, 20], "theta": [9, 10, 11, 17, 18, 19, 20], "ernst": [9, 11, 20], "theta_": [9, 11, 20], "prepar": [9, 18], "ir": [9, 11], "ti": [9, 11, 18], "iron": [9, 11, 15], "oxygen": [9, 11], "versu": [9, 11, 14], "deoxygen": [9, 11], "blood": [9, 11], "chemcial": 9, "environ": [9, 11, 25], "atom": [9, 11, 24], "local": [9, 11, 22], "consider": 9, "ppm": [9, 11, 16], "intra": 9, "spectral": 9, "agent": 9, "gadolinium": [9, 11], "gd": [9, 11], "shorten": [9, 11], "shape": [9, 17, 23], "product": 9, "tbw": [9, 19, 23], "thick": 9, "f_": [9, 11, 14, 19, 20], "z_": [9, 19], "wise": 9, "cumul": [9, 22], "area": [9, 11, 12, 18, 20, 22], "seq": [9, 20], "mea": [9, 20], "resolut": [9, 23], "rel": [9, 11, 12, 15, 16, 17, 20], "volumetr": 9, "coverag": 9, "multislic": [9, 18], "fse": 9, "tse": 9, "rare": 9, "subsequ": 9, "mai": [9, 18], "autocalibr": 9, "compress": [9, 18, 21], "sens": [9, 18, 21], "coeffici": [9, 12, 20], "deep": [9, 18], "learn": [9, 18], "dataset": [9, 18], "comparison": 9, "physicist": 10, "felix": 10, "who": 10, "won": 10, "nobel": 10, "prize": 10, "discoveri": 10, "phenomena": 10, "almost": 10, "behavior": [10, 14, 17, 19], "seen": [10, 11], "deriv": [10, 12, 14, 24], "kei": [10, 14, 16, 19], "interact": [10, 11, 14, 15, 18, 23, 24], "gnuplot": [10, 14, 23, 24], "graphic": [10, 14, 23, 24], "toolkit": [10, 14, 23, 24], "discourag": [10, 14, 23, 24], "activ": [10, 14, 16, 17, 23, 24, 25], "maintain": [10, 14, 23, 24], "limit": [10, 11, 12, 14, 18, 19, 20, 23, 24], "ulik": [10, 14, 23, 24], "fix": [10, 11, 14, 19, 23, 24], "commun": [10, 14, 23, 24], "pipe": [10, 14, 23, 24], "pass": [10, 14, 23, 24], "octav": [10, 14, 23, 24], "interpret": [10, 14, 23, 24], "reflect": [10, 11, 14, 23, 24], "manag": [10, 14, 23, 24], "mous": [10, 14, 23, 24], "click": [10, 14, 23, 24], "notifi": [10, 14, 23, 24], "intern": [10, 11, 14, 23, 24], "list": [10, 13, 14, 23, 24], "open": [10, 14, 15, 17, 23, 24], "qt": [10, 14, 23, 24], "respons": [10, 14, 19], "vast": 10, "major": [10, 11, 19, 20], "beavhior": 10, "longitudin": [10, 11, 18, 24], "lattic": [10, 11, 18, 24], "valuabl": [10, 24], "onlin": 10, "hand": [10, 16], "observ": [10, 12, 24], "neglect": [10, 14, 18, 22], "rightarrow": [10, 12], "infti": [10, 12, 22], "thin": 10, "5e3": 10, "1500": [10, 11], "mt": [10, 14, 16, 19], "unit": [10, 11, 13, 16, 19], "bloch_rot": [10, 19], "mstart": 10, "bstatic": 10, "1e": [10, 16], "ns": 10, "300": 10, "mall": [10, 24], "legend": [10, 11, 19, 20, 23, 24], "north": [10, 24], "boxoff": [10, 24], "5540": [10, 24], "oscil": [10, 16, 18, 23, 24], "orthogon": 10, "b_": [10, 16, 18], "energi": [10, 11, 15, 16, 19, 23, 24], "good": [10, 11, 13, 19], "progress": 10, "simplif": [10, 22], "f_0": [10, 11, 14, 16, 24], "stationari": 10, "represent": [10, 17, 18, 22], "now": [10, 14, 19, 22, 23, 24], "analysi": [10, 14], "45": [10, 18], "90": [10, 18, 19, 20], "default": [10, 24], "Then": [10, 11, 14, 23], "button": [10, 24], "go": 10, "creation": [10, 15], "gammabar": [10, 14, 19], "khz": [10, 14, 16, 18, 19], "simplic": [10, 14], "f0": [10, 19], "m0": [10, 11, 19, 20, 24], "m_equilibrium": [10, 19], "paaramet": 10, "t_rf": 10, "4000": [10, 11], "rf_flip_angl": 10, "radian": [10, 18], "b10": [10, 19], "425": 10, "8713e": 10, "03": 10, "12": [10, 16, 18, 23], "513": 10, "omega_0": 10, "northwest": 10, "192": 10, "clearli": 10, "438": 10, "equilibriuam": 10, "ultim": [10, 15], "orient": [10, 16, 24], "same": [10, 11, 14, 16, 18, 19], "shorthand": [10, 13], "complex": [10, 11, 13, 14], "adjust": [10, 24], "situat": [10, 14, 18], "millitesla": [10, 16], "tip": [10, 13, 17, 19, 24], "m_start": [10, 24], "bloch_rftip": 10, "bloch_relax": [10, 24], "1232e": 10, "17": 10, "0000e": 10, "00": 10, "num2str": [10, 11, 12, 16, 20], "657": 10, "rich": 11, "varieti": 11, "arguabl": [11, 19], "advantag": [11, 18, 19], "desir": [11, 19, 20], "intrins": 11, "molecular": 11, "signific": [11, 17], "precis": [11, 19], "quantum": 11, "human": [11, 18, 24], "divid": [11, 14, 16, 24], "liquid": [11, 15], "fluid": 11, "solid": 11, "cortic": 11, "bone": 11, "tendon": 11, "fibrosi": 11, "proteinac": 11, "organ": 11, "exchang": 11, "surround": [11, 16], "motion": [11, 18], "characterist": [11, 20], "transfer": [11, 21], "longer": [11, 18, 20], "lipid": [11, 23, 24], "shorter": [11, 14, 18, 20], "edema": 11, "lose": 11, "freedom": 11, "macromolecul": 11, "coupl": [11, 13], "stronger": [11, 15, 16], "microscop": 11, "molecul": [11, 23], "macroscop": 11, "cannot": [11, 18, 24], "caus": [11, 15, 19, 24], "import": [11, 17, 19, 20], "deposit": [11, 15, 23], "presenc": [11, 19], "calcif": 11, "calcium": 11, "vs": [11, 19], "hemoglobin": 11, "vein": 11, "basi": [11, 22, 24], "bold": 11, "brain": 11, "matter": 11, "790": 11, "920": 11, "100": [11, 14, 15, 16, 18, 19], "cerebrospin": 11, "csf": 11, "2000": 11, "arteri": 11, "1200": 11, "50": [11, 16], "liver": 11, "parenchyma": 11, "490": 11, "lung": 11, "830": 11, "myocardium": 11, "870": 11, "skelet": 11, "muscl": 11, "260": 11, "handbook": 11, "800": [11, 20], "110": 11, "1300": 11, "3700": 11, "1700": 11, "1000": [11, 18], "30": 11, "400": [11, 20], "cartilag": 11, "pictur": 11, "control": [11, 19, 20], "se": [11, 18], "200": 11, "t2v": 11, "130": 11, "s_te": 11, "150": 11, "mesh": [11, 14], "155": 11, "colorbar": [11, 16, 23], "incomplet": 11, "simplest": 11, "reach": 11, "acqrui": 11, "maxim": 11, "evolut": 11, "ntr": 11, "500": [11, 23], "nt_per_tr": 11, "t_per_tr": 11, "t_minu": 11, "t_plu": 11, "mz_minu": 11, "mz_plu": 11, "ep": [11, 19], "mz_all": 11, "o": 11, "t1v": 11, "s_tr": 11, "2500": 11, "s_flip": 11, "Not": 11, "enough": [11, 15, 17], "amount": [11, 12, 17, 19], "therebi": 11, "discuss": [11, 16], "principl": [11, 14, 16], "smaller": [11, 16], "boost": 11, "leav": 11, "certain": [11, 15], "ratio": [11, 13, 16, 24], "zoom": 11, "delai": 11, "strategi": [11, 14], "null": 11, "stir": 11, "attenu": 11, "flair": 11, "flip1": 11, "flip2": 11, "750": 11, "mz1_minu": 11, "mz2_minu": 11, "mz1_plu": 11, "mz2_plu": 11, "t1_minu": 11, "t1_plu": 11, "t2_minu": 11, "t2_plu": 11, "evolv": [11, 23], "find": [11, 12, 23], "2001": 11, "4001": 11, "6001": 11, "751": 11, "2751": 11, "4751": 11, "s_ti": 11, "chelat": 11, "superparamagnet": 11, "oxid": 11, "wherev": 11, "quantifi": 11, "r_1": 11, "r_2": 11, "typiclali": 11, "l": [11, 12], "mmol": 11, "cm": [11, 16, 23], "concentr": 11, "mm": 11, "hydrogen": [11, 24], "exploit": 11, "isol": [11, 16], "model": [11, 12], "peak": [11, 14, 19], "part": [11, 24], "million": 11, "220": 11, "hz": [11, 13, 14, 16, 18, 23, 24], "440": 11, "dixon": [11, 18], "realiti": [11, 17], "account": [11, 19, 20], "fatti": 11, "three": [11, 20], "circular": 11, "jinc": 11, "circl": 11, "circ": 11, "k_r": 11, "signal_gr": 11, "mrsignal_spoiled_gradient_echo": [11, 20], "contrast_phantom": 11, "nphan": 11, "xc": 11, "yc": 11, "25": 11, "1e3": [11, 14, 23], "06": 11, "64": [11, 12, 16], "ball": 11, "radiu": [11, 16], "20": [11, 19, 23], "160": 11, "3000": 11, "coordin": 11, "ad": [11, 17, 18, 19], "togeth": [11, 16, 19, 20], "individu": [11, 14, 16, 24], "exponenti": [11, 24], "displai": 11, "tan": 12, "funcion": 12, "ne": 12, "dx": 12, "ax": [12, 17], "ast": 12, "dirac": 12, "comb": 12, "sha": 12, "\u0448": 12, "rectangl": [12, 17], "sqcap": 12, "quad": 12, "normal": [12, 20], "intuit": [12, 14], "slid": 12, "nice": [12, 21], "unitari": 12, "ordinari": 12, "dk_x": 12, "dy": 12, "f_x": 12, "f_y": 12, "finit": 12, "kspace": 12, "w_": [12, 18], "accord": [12, 18], "convolv": [12, 14], "notabl": 12, "decomposit": 12, "512": 12, "kxmax": 12, "128": 12, "kxmax_trunc": 12, "fftshift": [12, 19], "ifft": 12, "ifftshift": 12, "power": [12, 14, 15, 16, 18, 19, 20, 21, 22], "actual": [12, 17], "dft": 12, "x_n": 12, "k_n": 12, "formula": 12, "extend": [12, 20], "si": 13, "gyromagnet": [13, 16, 24], "g_z": [13, 18, 23], "b_x": [13, 16], "b_y": [13, 16], "b_z": [13, 16, 22], "jargon": 13, "intimid": [13, 14], "imped": 13, "luckili": 13, "radiopaedia": 13, "articl": 13, "abbrevi": 13, "vendor": 13, "com": 13, "serv1": 13, "php": 13, "cam": 13, "format": 14, "equiat": 14, "impact": [14, 20], "affect": [14, 20], "resonnac": 14, "obtain": 14, "int": 14, "reason": [14, 20], "clear": 14, "soon": [14, 22], "add": [14, 15, 16, 23], "easiest": 14, "c_n": 14, "s_n": 14, "receiev": 14, "integr": [14, 19, 20, 22], "upsilon": 14, "gxr": [14, 18], "kx0": 14, "upsilon_cartesian": 14, "tesp": 14, "dky": 14, "deadtim": 14, "tall": 14, "upsilon_epi": 14, "corrupt": 14, "convolut": 14, "w_cartesian": 14, "w_epi": 14, "x0": 14, "height": 14, "outsid": [14, 19], "get": [14, 17, 24], "wors": 14, "speci": 14, "examin": [14, 20], "could": 14, "index": 14, "complic": 14, "gain": [14, 18, 20], "look": [14, 15, 17, 18, 19, 24], "_0": [14, 22], "r_0": 14, "star": 14, "df": [14, 19, 23], "frfom": 14, "side": [14, 16, 20], "lobe": 14, "interpol": [14, 20], "write": 14, "version": [14, 23], "numer": [14, 20], "solver": 14, "graph": 14, "As": [14, 19, 24], "framework": [14, 22], "express": 14, "spread": [14, 19], "psf": 14, "impuls": 14, "boil": 14, "down": [14, 19, 24], "decompos": [14, 20], "m_i": 14, "w_i": 14, "sum_i": 14, "m_1": 14, "m_2": 14, "w_1": 14, "w_2": 14, "accur": 14, "thw": 14, "flow": [14, 22], "explor": 15, "deconstruct": 15, "insid": 15, "insight": 15, "loud": 15, "danger": 15, "metal": 15, "cut": 15, "greater": 15, "tesla": 15, "manget": [15, 24], "superconduct": 15, "alloi": 15, "bath": 15, "helium": 15, "dager": 15, "ferromagnet": [15, 18], "suck": 15, "antenna": 15, "electromagnet": [15, 16, 24], "perturb": [15, 16, 24], "releas": 15, "radio": [15, 16], "mhz": [15, 16, 18], "excitaiton": [15, 18], "thermal": [15, 24], "linearli": [15, 20, 22], "switch": [15, 16, 17, 19, 24], "current": 15, "exert": 15, "forc": 15, "lorentz": 15, "vibrat": 15, "place": [15, 16, 18, 24], "fiel": 15, "distinguish": 15, "critic": [16, 20], "summar": [16, 20], "mu": [16, 18, 24], "wire": 16, "govern": [16, 24], "maxwel": 16, "rule": 16, "link": 16, "solenoid": 16, "ensur": 16, "usual": [16, 17, 18], "never": 16, "perfect": 16, "ll": 16, "few": [16, 19, 21], "Their": 16, "00001": 16, "perpedicularli": 16, "plane": [16, 17, 18], "reactiv": 16, "capacitor": 16, "inductor": 16, "kw": 16, "mv": 16, "aris": [16, 18], "channel": 16, "put": [16, 20, 22], "i0": 16, "amp": 16, "mu0": 16, "401": 16, "bz": 16, "211": [16, 19, 23], "212": [16, 19, 23], "resons": 16, "event": 16, "amplifi": 16, "digit": 16, "tell": 16, "birdcag": 16, "perpendicular": [16, 18, 24], "tailor": 16, "knee": 16, "abdomen": 16, "head": 16, "configur": [16, 18], "decoupl": 16, "detun": 16, "don": 16, "senit": 16, "move": [16, 18, 24], "brightest": 16, "biot": 16, "savart": 16, "law": 16, "flag_2d": 16, "just": [16, 21], "bx": 16, "BY": 16, "xp": 16, "zp": 16, "loop_coil_field": 16, "18": 16, "bmag": 16, "xhalf": 16, "chapter": [17, 24], "indic": 17, "conjunct": 17, "remeb": 17, "incred": [17, 22], "convei": 17, "experiment": 17, "speed": 17, "drawn": 17, "bracket": 17, "simlifi": 17, "crusher": 17, "destruct": 17, "instantan": 17, "slew": [17, 23], "trapezoid": 17, "3t": 18, "5t": 18, "xrai": 18, "visibl": 18, "fm": 18, "am": 18, "proper": 18, "assign": 18, "conduct": 18, "isotop": 18, "1h": 18, "13": [18, 24], "19": [18, 24], "2h": 18, "diamagnet": 18, "paramagnet": 18, "immedi": 18, "equilibirum": 18, "lab": [18, 19], "frame": [18, 19], "flux": 18, "benefit": 18, "doesn": 18, "contribut": [18, 24], "highest": 18, "2e": 18, "pdw": 18, "t1w": 18, "t2w": 18, "additoin": 18, "daq": 18, "serv": 18, "statement": 18, "true": 18, "overlap": 18, "prewind": 18, "\u03b8": 18, "twice": 18, "thinner": 18, "decreas": 18, "bw": [18, 19], "theorem": 18, "avoid": 18, "lowest": 18, "oversampl": 18, "3dft": 18, "anti": 18, "fov_x": 18, "none": 18, "stretch": [18, 19], "pile": 18, "bright": 18, "rapidli": 18, "robust": 18, "intravoxel": 18, "gather": 18, "databas": 18, "outer": 18, "amplif": 18, "acquist": 18, "Of": 18, "regardless": 18, "develop": 18, "000": 18, "decod": 18, "recurr": 18, "appl": 19, "detail": 19, "distanc": 19, "absorb": 19, "heat": 19, "safeti": 19, "minim": 19, "sinusoid": 19, "002": 19, "tmax": 19, "rf_sinusoid": 19, "ft_sinusoid": 19, "imaginari": 19, "tmat": 19, "dfmat": 19, "rf_all": 19, "rf_n": 19, "ft_n": 19, "fwidth": 19, "11": [19, 23], "rf_sinc": 19, "ft_sinc": 19, "gz": [19, 23], "poorli": 19, "uniformli": 19, "forth": [19, 24], "substanti": 19, "meanwhil": 19, "wide": [19, 20], "wherea": [19, 24], "360": 19, "address": 19, "impli": [19, 20], "shrunk": 19, "bwplot": 19, "IN": 19, "rf_shape": 19, "trf": 19, "bwrf": 19, "plai": 19, "notic": [19, 24], "sharper": 19, "But": [19, 20], "break": 19, "sophist": 19, "shinnar": 19, "le": 19, "roux": 19, "slr": 19, "dzrf": [19, 23], "isn": 19, "issu": 19, "themselv": 19, "subtli": 19, "degrad": 19, "inv": 19, "theoret": 20, "foundat": 20, "delta_i": 20, "delta_z": 20, "gaussian": 20, "root": 20, "sigma": 20, "downtim": 20, "intrigu": 20, "trdt1": 20, "01": 20, "1600": 20, "inf": 20, "theta_optim": 20, "snr_effici": 20, "it1": 20, "aco": 20, "drop": 20, "stabl": 20, "finer": 20, "coarser": 20, "nativ": 20, "pad": 20, "nearbi": 20, "scale": [20, 23], "care": 20, "taken": 20, "demonin": 20, "tread": 20, "snr_t2s_onesid": 20, "imax_onesid": 20, "snr_t2s_twosid": 20, "imax_twosid": 20, "disp": 20, "2806": 20, "4907": 20, "ve": 21, "favorit": 21, "focus": 21, "kmjohnson3": 21, "intro": 21, "python": 21, "jupyt": [21, 25], "introduct": 21, "mribri999": 21, "mrsignalsseq": 21, "cours": 21, "lectur": 21, "introductori": 21, "marku": 21, "nilsson": 21, "matlab": 21, "mikgroup": 21, "sigpi": 21, "packag": 21, "mrirecon": 21, "bart": 21, "toolbox": 21, "qmrlab": 21, "quantit": 21, "fit": 21, "ismrm": 21, "mrhub": 21, "hub": 21, "worth": 21, "brows": 21, "delv": [21, 24], "topic": 21, "sort": 22, "stop": 22, "undo": 22, "motiv": 22, "rather": 22, "textrm": 22, "i2": 22, "amaz": 22, "appropri": 22, "spectroscopi": 23, "relat": 23, "reveal": 23, "travers": 23, "psace": 23, "trick": 23, "compil": 23, "abr": 23, "mex": 23, "file": 23, "error": 23, "re": 23, "run": 23, "abrx": 23, "31": [23, 24], "column": 23, "trajectoi": 23, "nlobe": 23, "nspec": 23, "nramp": 23, "ramp": 23, "g1": 23, "gamp": 23, "95": 23, "mod": 23, "nrw": 23, "grw": 23, "cumsum": 23, "k_f": 23, "h_f": 23, "h_z": 23, "envelop": 23, "subpuls": 23, "4258": 23, "slewmax": 23, "15e3": 23, "gmax": 23, "20e": 23, "sbw": 23, "dz": 23, "10e": 23, "verse_frac": 23, "nspat": 23, "nwait": 23, "rfspec": 23, "gf": 23, "ab2ex": 23, "g_f": 23, "rfspat": 23, "min": 23, "ceil": 23, "floor": 23, "vers": 23, "rfspatv": 23, "isnan": 23, "g1z": 23, "mxy_z": 23, "flip_scal": 23, "rfscaleg": 23, "589": 23, "mxy_2d": 23, "m_xy": 23, "watch": 23, "behav": 24, "phenomenom": 24, "nucleu": 24, "angular": 24, "momentum": 24, "moment": 24, "act": 24, "respond": 24, "tyipcal": 24, "nuclei": 24, "primari": 24, "23": 24, "na": 24, "p": 24, "abund": 24, "absenc": 24, "randomli": 24, "ensembl": 24, "arrow": 24, "vertic": 24, "www": 24, "planck": 24, "63e": 24, "34": 24, "58e6": 24, "boltzmann": 24, "62e": 24, "ev": 24, "38e": 24, "temperatur": 24, "310": 24, "prefer": 24, "boltzman": 24, "uparrow": 24, "downarrow": 24, "kt": 24, "expon": 24, "strongli": 24, "analog": 24, "swing": 24, "your": 24, "leg": 24, "wrong": 24, "compassmr": 24, "compass": 24, "mode": 24, "slider": 24, "freq": 24, "uenci": 24, "new": 24, "checkbox": 24, "hit": 24, "push": 24, "needl": 24, "blue": 24, "trace": 24, "highlight": 24, "composit": 24, "last": 24, "mx": 24, "anaconda": 25, "prompt": 25, "FOR": 25, "conda": 25, "wintest": 25, "pip": 25, "instal": 25, "forg": 25, "octave_kernel": 25, "jb": 25, "booknam": 25, "runjb": 25, "quantecon": 25, "mini": 25, "seem": 25}, "objects": {}, "objtypes": {}, "objnames": {}, "titleterms": {"acceler": [0, 9, 18], "imag": [0, 1, 3, 6, 8, 9, 11, 18, 22], "method": [0, 9, 18], "learn": [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14, 15, 16, 17, 19, 20, 22, 23, 24], "goal": [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14, 15, 16, 17, 19, 20, 22, 23, 24], "gener": 0, "formul": 0, "mri": [0, 6, 7, 9, 11, 12, 13, 14, 15, 16, 18, 21, 22], "reconstruct": [0, 6, 18], "partial": 0, "fourier": [0, 6, 12], "parallel": 0, "model": 0, "base": 0, "linear": 0, "predict": 0, "snr": [0, 18, 20], "artifact": [0, 1, 9, 18], "compress": 0, "sens": 0, "deep": 0, "requir": 0, "dl": 0, "refer": 0, "introduct": [1, 7], "comparison": 1, "displac": 1, "motion": 1, "flow": 1, "exampl": [1, 10, 11, 12], "alias": 1, "distort": 1, "t2": [1, 5, 11], "simul": [1, 5, 10, 16, 24], "field": [2, 13, 15, 16, 17, 22], "view": 2, "fov": [2, 18], "resolut": [2, 18, 20], "spatial": [2, 9, 18, 22, 23], "fast": [3, 9, 18], "puls": [3, 4, 5, 9, 10, 17, 18, 19, 23], "sequenc": [3, 5, 9, 17, 18], "multipl": 3, "spin": [3, 5, 9, 24], "echo": [3, 5], "rare": 3, "fse": 3, "tse": 3, "simplifi": [3, 17], "diagram": [3, 17], "paramet": [3, 17], "tradeoff": 3, "planar": 3, "epi": 3, "k": [3, 6, 8, 12, 14, 22], "space": [3, 6, 8, 12, 13, 14, 22], "gradient": [3, 5, 15, 16, 17, 22], "spoiler": 3, "crusher": 3, "rf": [3, 4, 9, 10, 15, 16, 17, 18, 19, 23], "spoil": 3, "type": 3, "fun": 4, "adiabat": 4, "pretti": 4, "pictur": 4, "ge": 5, "gre": 5, "off": [5, 14, 19], "reson": [5, 14, 16, 19, 24], "effect": [5, 22], "refocus": 5, "visual": 5, "se": 5, "sort": 6, "data": [6, 12, 14, 17, 20, 22], "transform": [6, 12], "principl": 7, "get": 7, "start": 7, "cours": 7, "lectur": 7, "us": 7, "educ": 7, "resourc": [7, 21], "code": 7, "acknowledg": 7, "encod": [8, 9, 18, 22], "cartesian": [8, 22], "frequenc": [8, 22, 24], "phase": [8, 22], "ft": [8, 9, 22], "trajectori": [8, 22], "kei": [9, 17], "concept": [9, 12], "equat": [9, 10, 14, 20, 24], "background": 9, "materi": 9, "mr": [9, 18], "physic": [9, 18, 24], "system": [9, 15, 16, 18], "experi": [9, 15], "contrast": [9, 11, 18], "In": 9, "vivo": 9, "characterist": [9, 18], "bloch": 10, "THE": 10, "precess": [10, 24], "excit": [10, 16, 17, 19, 24], "constant": 10, "amplitud": 10, "lab": 10, "versu": [10, 19, 20], "rotat": 10, "frame": 10, "common": 10, "flip": [10, 11, 19], "angl": [10, 11, 19], "relax": [10, 14, 24], "what": 11, "determin": 11, "t1": 11, "valu": 11, "typic": 11, "1": 11, "5": 11, "t": [11, 15, 16], "3": 11, "te": 11, "tr": [11, 20], "90": 11, "degre": 11, "proton": 11, "densiti": 11, "weight": [11, 14], "pd": 11, "invers": [11, 12], "recoveri": 11, "agent": 11, "fat": 11, "water": 11, "simpl": 11, "phantom": 11, "challeng": 11, "yourself": 11, "math": 12, "complex": 12, "number": 12, "impuls": 12, "function": 12, "train": 12, "sampl": [12, 17], "other": 12, "convolut": 12, "2": 12, "d": 12, "n": 12, "dualiti": 12, "separ": 12, "ident": 12, "pair": 12, "truncat": 12, "point": 12, "spread": 12, "psf": 12, "analysi": 12, "discret": 12, "notat": 13, "terminolog": 13, "definit": 13, "posit": 13, "net": 13, "magnet": [13, 15, 16, 17, 20, 22, 24], "acronym": 13, "glossari": 13, "The": [14, 15, 17], "signal": [14, 16, 20, 22], "ideal": 14, "ad": 14, "coil": [14, 15, 16, 18], "sensit": [14, 16], "dure": 14, "acquisit": [14, 17, 20], "chemic": 14, "shift": [14, 19], "complet": 14, "compon": [15, 17], "scanner": 15, "main": [15, 16], "b_0": [15, 16], "radiofrequ": [15, 16], "b_1": [15, 16], "vec": [15, 16], "r": [15, 16], "g": [15, 16], "fundament": 15, "procedur": 15, "loop": 16, "current": 16, "transmit": 16, "tx": 16, "receiv": 16, "rx": 16, "recept": 16, "creat": 16, "reciproc": 16, "profil": 16, "element": 16, "local": 17, "g_x": 17, "g_y": 17, "g_z": 17, "window": 17, "daq": 17, "annot": 17, "question": 18, "properti": 19, "time": [19, 20], "bandwidth": 19, "product": 19, "slice": 19, "thick": 19, "specif": 19, "absorpt": 19, "rate": 19, "select": 19, "hard": 19, "shape": 19, "On": 19, "design": [19, 23], "high": 19, "nois": 20, "ratio": 20, "depend": 20, "voxel": 20, "volum": 20, "transvers": 20, "effici": 20, "post": 20, "process": 20, "upsampl": 20, "downsampl": 20, "t_2": 20, "decai": 20, "softwar": 21, "from": 22, "spectral": 23, "nuclear": 24, "polar": 24, "equilibrium": 24, "fraction": 24}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 6, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx": 56}})
\ No newline at end of file
+Search.setIndex({"docnames": ["Accelerated Imaging Methods", "Artifacts", "FOV and Resolution", "Fast Imaging Pulse Sequences", "Fun with RF Pulses", "Gradient and Spin Echoes", "Image Reconstruction", "Introduction", "K-space", "Key MRI Concepts", "MR Physics - Bloch Equation", "MRI Contrast", "MRI Math Concepts", "MRI Notation", "MRI Signal Equation", "MRI System", "Magnetic Fields and RF Coils", "Pulse Sequence", "Questions", "RF Pulses", "Signal to Noise Ratio", "Software_Resources", "Spatial Encoding", "Spectral-Spatial RF Pulses", "Spin Physics", "build_notes"], "filenames": ["Accelerated Imaging Methods.ipynb", "Artifacts.ipynb", "FOV and Resolution.ipynb", "Fast Imaging Pulse Sequences.ipynb", "Fun with RF Pulses.ipynb", "Gradient and Spin Echoes.ipynb", "Image Reconstruction.ipynb", "Introduction.md", "K-space.ipynb", "Key MRI Concepts.md", "MR Physics - Bloch Equation.ipynb", "MRI Contrast.ipynb", "MRI Math Concepts.ipynb", "MRI Notation.ipynb", "MRI Signal Equation.ipynb", "MRI System.ipynb", "Magnetic Fields and RF Coils.ipynb", "Pulse Sequence.ipynb", "Questions.md", "RF Pulses.ipynb", "Signal to Noise Ratio.ipynb", "Software_Resources.md", "Spatial Encoding.ipynb", "Spectral-Spatial RF Pulses.ipynb", "Spin Physics.ipynb", "build_notes.md"], "titles": ["Accelerated Imaging Methods", "Artifacts", "Field of View (FOV) and Resolution", "Fast Imaging Pulse Sequences", "Fun with RF Pulses?", "Gradient and Spin Echo Pulse Sequences", "Image Reconstruction", "Introduction to Principles of MRI", "K-space", "Key MRI Concepts and Equations", "Bloch Equation", "MRI Contrast", "MRI Math Concepts", "MRI Notation and Terminology", "The MRI Signal Equation and K-space", "The MRI System", "Magnetic fields in MRI", "The Pulse Sequence", "MRI Questions", "RF Pulses", "Signal to Noise Ratio (SNR)", "MRI Software Resources", "Spatial Encoding", "Spectral-Spatial RF Pulses", "Spin Physics", "&lt;no title&gt;"], "terms": {"scan": [0, 3, 7, 9, 15, 16, 18, 20], "can": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "appli": [0, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 17, 18, 19, 20, 22, 23, 24], "reduc": [0, 3, 5, 11, 18], "number": [0, 3, 10, 13, 14, 17, 23, 24], "k": [0, 1, 2, 9, 11, 18, 20, 23, 24], "space": [0, 1, 2, 9, 11, 16, 18, 20, 23], "sampl": [0, 1, 2, 6, 8, 9, 14, 18, 21, 22, 23], "also": [0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 19, 20, 22, 23, 24], "known": [0, 3, 6, 8, 11, 12, 14, 15, 16, 22, 24], "undersampl": [0, 18], "These": [0, 1, 2, 3, 4, 5, 8, 11, 14, 15, 16, 19, 23, 24], "correspond": [0, 6, 8, 18], "advanc": [0, 6, 11, 21], "allow": [0, 3, 11, 12, 19, 20], "The": [0, 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 16, 18, 19, 20, 22, 23, 24], "techniqu": [0, 3, 6, 8, 11], "cover": [0, 1, 8, 9, 24], "here": [0, 1, 4, 7, 10, 12, 14, 17, 22, 24], "includ": [0, 1, 3, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 20, 21, 23, 24], "describ": [0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "how": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "ar": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], "form": [0, 2, 3, 6, 7, 8, 11, 14, 15, 17, 19, 22, 23, 24], "work": [0, 3, 7, 8, 9, 11, 15, 23], "understand": [0, 3, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 24], "constraint": [0, 7, 14, 20], "tradeoff": [0, 7, 14, 20], "identifi": [0, 1, 3, 5, 7, 11, 14, 17, 18, 23], "when": [0, 3, 4, 5, 9, 10, 11, 12, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24], "manipul": [0, 2, 3, 6, 7, 11, 14, 16, 17, 19, 20], "sequenc": [0, 1, 2, 6, 7, 8, 11, 13, 14, 16, 19, 20, 21], "paramet": [0, 2, 6, 7, 9, 10, 11, 14, 19, 20, 23], "improv": [0, 2, 3, 6, 7, 11, 14, 18, 19, 20], "perform": [0, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 15, 16, 17, 18, 19, 20], "defin": [0, 1, 2, 6, 8, 9, 12, 14, 16, 17, 19, 20, 22, 24], "which": [0, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "modifi": [0, 1], "analyz": [0, 1, 6, 7, 10, 12, 14, 17, 19], "data": [0, 1, 3, 5, 7, 8, 9, 11, 15, 18], "an": [0, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "from": [0, 1, 3, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 19, 20, 21, 23, 24], "raw": [0, 6], "For": [0, 1, 2, 6, 7, 10, 11, 12, 14, 17, 18, 19, 20, 22, 23, 24], "help": [0, 13, 14, 17, 23, 24], "reformul": 0, "problem": [0, 18], "system": [0, 1, 6, 12, 20, 21], "us": [0, 1, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "standard": [0, 13], "mathemat": [0, 1, 16], "notat": [0, 10, 14, 16, 22], "y": [0, 4, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20], "mathbf": 0, "e": [0, 1, 3, 6, 8, 9, 10, 11, 14, 16, 17, 18, 19, 22, 24], "x": [0, 2, 4, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 23], "n": [0, 1, 2, 8, 9, 10, 11, 14, 16, 17, 19, 24], "where": [0, 1, 8, 10, 11, 12, 14, 15, 16, 17, 19, 20, 23, 24], "acquir": [0, 3, 5, 6, 8, 9, 11, 14, 15, 18, 20, 22], "encod": [0, 1, 3, 5, 14, 15, 16, 17], "matrix": [0, 6, 11, 22], "spatial": [0, 1, 5, 8, 12, 14, 15, 16, 17, 20], "distribut": [0, 20, 24], "transvers": [0, 3, 5, 6, 8, 9, 10, 11, 13, 14, 16, 17, 18, 22, 23, 24], "magnet": [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 18, 19, 21, 23], "g": [0, 1, 3, 6, 8, 9, 11, 12, 13, 14, 17, 18, 19, 22, 23], "nois": [0, 1, 15, 16, 18], "In": [0, 1, 2, 4, 6, 7, 8, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 24], "thi": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24], "vector": [0, 4, 10, 16, 19, 24], "exampl": [0, 2, 4, 5, 6, 14, 20, 21, 23, 24, 25], "2d": [0, 5, 6, 8, 9, 16, 18, 23], "ft": [0, 12, 18], "would": [0, 1, 6, 7, 10, 15, 23, 24], "convert": [0, 6, 9, 10, 19], "left": [0, 4, 6, 10, 12, 14, 16, 22], "begin": [0, 5, 9, 10, 12, 13, 16, 20, 22, 24], "arrai": [0, 9, 12, 16, 18], "c": [0, 1, 12, 18, 24, 25], "s_1": 0, "t_1": [0, 9, 10, 11, 13, 14, 18, 20, 24], "t_2": [0, 5, 9, 10, 11, 13, 14, 18, 22, 24], "vdot": 0, "t_": [0, 1, 3, 9, 10, 17, 18, 19, 20], "nx": 0, "s_2": 0, "s_": [0, 5, 9, 11, 14], "ny": 0, "end": [0, 2, 5, 8, 9, 10, 11, 12, 13, 16, 19, 20, 22, 23, 24], "right": [0, 4, 12, 14, 22, 24], "s_m": 0, "t_n": 0, "m": [0, 5, 6, 8, 9, 10, 11, 13, 14, 16, 18, 19, 22, 24], "th": [0, 6], "tr": [0, 1, 3, 6, 9, 14, 17, 18], "x_1": 0, "y_1": 0, "x_2": 0, "x_": 0, "1": [0, 1, 2, 5, 6, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 22, 23, 24], "y_2": 0, "y_": 0, "x_i": 0, "y_i": 0, "equal": [0, 1, 2, 11, 18, 19], "locat": [0, 1, 2, 5, 6, 8, 10, 11, 12, 14, 15, 16, 19, 22, 24], "minimum": [0, 16, 17, 18], "discret": [0, 6], "transform": [0, 8, 9, 10, 11, 14, 18, 19, 22, 23], "f": [0, 1, 6, 8, 9, 11, 12, 14, 15, 18, 19, 22, 23, 24], "repres": [0, 5, 9, 11, 12, 14, 16, 18, 19, 22, 24], "our": [0, 2, 5, 6, 10, 11, 12, 14, 15, 16, 22, 24], "evalu": [0, 6, 22], "entri": [0, 1], "being": [0, 1, 10, 14, 17, 19, 20, 24], "vec": [0, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 18, 22, 24], "_i": [0, 6], "r": [0, 1, 5, 6, 9, 10, 11, 13, 14, 18, 22, 24], "_j": 0, "_": [0, 6, 9, 14, 17, 22], "i": [0, 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23], "j": [0, 24], "exp": [0, 1, 5, 8, 9, 11, 12, 14, 18, 19, 20, 22], "2": [0, 1, 2, 4, 5, 8, 9, 10, 11, 14, 16, 17, 18, 19, 20, 22, 23, 24], "pi": [0, 1, 5, 8, 9, 10, 11, 12, 14, 16, 18, 19, 20, 22, 23], "cdot": [0, 9, 11, 12, 14, 16, 18, 19, 22], "case": [0, 11, 12, 14, 19, 20], "measur": [0, 5, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 22, 24], "invers": [0, 1, 4, 6, 8, 9, 14, 18, 19, 22], "fulli": [0, 6, 8, 11, 18], "well": [0, 1, 5, 6, 9, 11, 14, 16, 17, 19], "hat": [0, 11, 12, 14], "h": [0, 9, 12, 18, 23, 24], "fraction": 0, "nex": [0, 9, 18], "util": 0, "conjug": [0, 9, 18], "symmetri": [0, 9, 18], "properti": [0, 9, 10, 11, 12, 14, 18, 20, 23, 24], "state": [0, 3, 11, 18, 24], "real": [0, 8, 12, 18, 19, 23, 24], "valu": [0, 10, 12, 14, 18, 19, 20, 24], "function": [0, 1, 7, 10, 11, 14, 16, 18, 19, 22, 23], "ha": [0, 5, 6, 7, 9, 10, 11, 12, 14, 16, 17, 19, 23, 24], "If": [0, 7, 10, 12, 15, 24], "satisfi": [0, 9], "mathrm": [0, 5, 6, 9, 11, 12, 16, 17, 20, 22], "mathcal": [0, 6, 9, 11, 12, 14, 18, 22, 23], "im": 0, "0": [0, 1, 2, 5, 6, 8, 9, 10, 11, 12, 14, 16, 18, 19, 20, 22, 23, 24], "object": [0, 1, 2, 6, 8, 11, 12, 14, 22], "so": [0, 5, 8, 10, 11, 14, 15, 16, 19, 20, 23, 24], "conidit": 0, "align": [0, 5, 9, 15, 16, 18, 22, 24], "across": [0, 1, 3, 5, 10, 13, 14, 15, 16, 18, 19], "entir": [0, 1, 16, 21], "With": [0, 10, 23], "strict": 0, "definit": 0, "m_": [0, 1, 5, 6, 8, 9, 10, 13, 14, 17, 18, 19, 22, 23, 24], "xy": [0, 1, 5, 6, 8, 9, 10, 13, 14, 16, 17, 19, 22, 23, 24], "mean": [0, 5, 6, 8, 10, 11, 14, 16, 18, 19, 20, 22, 24], "all": [0, 3, 5, 7, 9, 10, 12, 14, 15, 16, 17, 18, 20, 24], "along": [0, 4, 7, 10, 17, 18, 19, 24], "m_x": [0, 10, 13, 24], "practic": [0, 3, 5, 8, 12, 20], "global": 0, "phase": [0, 1, 3, 4, 5, 9, 11, 14, 16, 18, 19, 22], "offset": [0, 20], "estim": [0, 11], "relationship": [0, 2, 11, 16, 19, 20], "hold": [0, 1, 18], "long": [0, 3, 9, 11, 20], "onli": [0, 8, 9, 12, 17, 18, 19, 23, 24], "half": [0, 2, 9, 18], "other": [0, 3, 4, 7, 8, 10, 14, 15, 16, 19, 20, 22, 24], "fill": 0, "time": [0, 3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 22, 23, 24], "faster": [0, 3, 18], "sourc": [0, 1, 9, 10, 11, 16, 24], "result": [0, 1, 4, 6, 10, 11, 12, 14, 15, 16, 19, 20, 22, 23, 24], "violat": [0, 23], "condit": [0, 11, 20, 24], "first": [0, 8, 10, 11, 17, 19, 22], "m_y": [0, 10, 13, 24], "sinc": [0, 1, 2, 5, 8, 11, 12, 14, 15, 16, 19, 20], "correct": [0, 1, 11, 16, 18, 19, 24], "more": [0, 1, 5, 6, 7, 9, 10, 11, 14, 15, 17, 18, 19, 20, 21], "problemat": 0, "come": [0, 7, 11, 22], "rf": [0, 1, 5, 8, 11, 13, 14, 20, 22], "coil": [0, 4, 9, 17, 19, 20, 22, 24], "profil": [0, 9, 14, 19, 23], "off": [0, 1, 2, 4, 9, 11, 15, 16, 17, 22, 24], "reson": [0, 1, 4, 7, 9, 10, 11, 15, 17, 18, 22], "chemic": [0, 1, 3, 9, 11, 18, 23], "shift": [0, 1, 3, 9, 11, 18, 23], "howev": [0, 3, 5, 11, 12, 14, 19, 20, 24], "much": [0, 1, 14, 16, 17, 18, 19, 24], "addit": [0, 5, 8, 10, 11, 14, 18, 19, 20], "typic": [0, 1, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 17, 18, 19, 20, 23], "contain": [0, 5, 18, 19], "low": [0, 3, 11, 14, 24], "frequenc": [0, 1, 3, 4, 5, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 22, 23], "especi": [0, 1, 20, 21], "main": [0, 1, 5, 9, 10, 11, 13, 14, 17, 18, 23, 24], "field": [0, 1, 3, 4, 5, 8, 9, 10, 11, 14, 18, 19, 20, 24], "inhomogen": [0, 1, 5, 9, 11, 14, 16, 18], "delta": [0, 1, 2, 5, 9, 11, 12, 14, 16, 19, 22, 24], "b_0": [0, 5, 9, 10, 11, 13, 14, 18, 24], "captur": [0, 2, 8, 11, 14, 15, 16, 17, 20], "central": 0, "thu": [0, 12, 14, 15, 16, 18, 19, 22, 24], "slightli": [0, 5, 9, 17, 19, 24], "than": [0, 9, 11, 16, 18], "special": [0, 4], "algorithm": [0, 6, 12, 23], "project": 0, "onto": [0, 14], "convex": 0, "set": [0, 7, 11, 12], "poc": 0, "homodyn": 0, "detect": [0, 9, 15, 16, 18, 24], "we": [0, 1, 2, 5, 6, 8, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 24], "need": [0, 9, 12, 15, 18, 20, 22, 24, 25], "consid": [0, 10, 11, 14, 19, 20, 24], "sensit": [0, 1, 3, 9, 15, 18, 22], "_q": 0, "each": [0, 3, 6, 11, 12, 14, 16, 17, 20], "sub": [0, 13, 23], "oper": [0, 12, 14, 18], "s": [0, 1, 5, 7, 9, 10, 11, 13, 14, 16, 18, 20, 22, 23, 24], "y_q": 0, "n_q": 0, "c_q": 0, "diagon": 0, "diagnoal": 0, "whether": [0, 1, 9], "expect": [0, 10, 11, 14, 17, 18, 20], "grid": [0, 6, 8], "wa": [0, 3, 5, 7], "It": [0, 3, 5, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 22, 24], "conveni": [0, 24], "point": [0, 14, 20, 24], "return": [0, 10, 15, 24], "origin": [0, 1, 3, 12, 14, 16, 24], "creat": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 15, 17, 18, 19, 22, 23, 24], "augment": 0, "matric": [0, 11, 14], "concaten": 0, "element": [0, 9, 14], "dimens": [0, 6, 8, 11, 12, 14, 20, 23], "ldot": [0, 8, 9], "y_n": 0, "_1": [0, 11], "_2": [0, 11], "_n": 0, "n_1": 0, "n_2": 0, "n_n": 0, "ex": [0, 19], "some": [0, 1, 4, 7, 8, 14, 16, 17, 19, 20], "simul": [0, 4, 7, 8, 11, 19, 21], "espirit": 0, "nlinv": 0, "singl": [0, 1, 3, 9, 11, 14, 16, 17, 18, 19, 22], "underli": 0, "solv": [0, 14], "optim": [0, 9, 11, 20], "popular": [0, 3, 5, 7, 21], "arg": 0, "min_": 0, "frac": [0, 1, 2, 5, 8, 9, 10, 11, 12, 18, 19, 20, 22, 24], "2_2": 0, "directli": [0, 11, 18], "pseudo": [0, 9, 18], "calcul": [0, 10, 18], "pattern": [0, 2, 8, 9, 11, 17, 18, 19], "regular": 0, "consist": [0, 8, 11, 15, 23], "skip": [0, 1, 9], "line": [0, 1, 2, 3, 6, 7, 8, 9, 10, 14, 16, 17, 18, 23], "assum": [0, 9, 14], "combin": [0, 14, 23], "inlcud": 0, "auto": 0, "smash": 0, "grappa": 0, "spirit": 0, "calibr": [0, 18], "kernel": [0, 14], "comput": [0, 12], "itself": 0, "follow": [0, 5, 6, 7, 8, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22], "lambda": 0, "tune": [0, 16], "ident": [0, 19], "simultan": [0, 9, 18], "enforc": 0, "term": [0, 10, 11, 14, 18], "self": 0, "sescond": 0, "either": [0, 14, 18, 19, 20], "iter": 0, "while": [0, 1, 5, 10, 11, 14, 15, 19, 20, 23], "full": [0, 2, 3, 7, 10, 13, 14, 18, 24], "center": [0, 3, 6, 8, 9, 11, 14, 16, 17, 18, 19], "There": [0, 1, 5, 10, 19, 20], "penalti": 0, "vari": [0, 8, 10, 11, 13, 14, 15, 16, 19, 20, 22, 23, 24], "sever": [0, 5], "depend": [0, 1, 5, 8, 10, 11, 14, 16, 18, 22, 24], "variat": [0, 4, 5, 8, 9, 15, 21, 22], "direct": [0, 1, 4, 8, 9, 10, 14, 16, 18, 23, 24], "lead": [0, 1, 3, 5, 9, 11, 12, 14, 19, 20, 22], "lower": [0, 11, 20], "convers": 0, "less": [0, 7, 9, 19, 24], "ill": 0, "higher": [0, 1, 11, 19, 20, 24], "penatli": 0, "region": [0, 1, 16], "littl": 0, "differ": [0, 1, 5, 6, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 24], "betweeen": 0, "bodi": [0, 11, 16, 18, 19, 24], "tend": 0, "have": [0, 1, 4, 9, 10, 11, 16, 18, 19, 20, 22, 24], "larger": [0, 1, 14, 16, 18], "character": [0, 1, 5, 8, 12, 14, 18, 19, 22], "factor": [0, 14, 18, 20], "geq": 0, "loss": [0, 1, 14, 18, 20], "load": [0, 1, 5, 6, 10, 11, 14, 15, 19, 20, 23, 24], "geometri": 0, "appyl": 0, "total": [0, 9, 18, 19, 20, 24], "readout": [0, 3, 6, 8, 14, 17, 18, 20], "sqrt": [0, 8, 9, 11, 12, 16, 18, 19, 20], "snr_": [0, 18, 20], "appear": [0, 1, 9, 11, 19], "alias": [0, 18], "sometim": [0, 10, 17], "complet": [0, 5, 7, 8, 10, 18], "remov": [0, 5, 10, 11, 14, 19, 20, 23], "like": [0, 7, 15, 19], "mismatch": 0, "between": [0, 3, 5, 9, 11, 14, 16, 17, 18, 19, 24], "cs": [0, 11, 14], "theori": [0, 12], "sai": [0, 16], "domain": [0, 8, 9, 12, 18, 22], "subset": 0, "word": [0, 4, 15, 19, 22], "further": [0, 14], "acquisit": [0, 3, 5, 6, 8, 9, 11, 15, 18, 22], "specif": [0, 1, 3, 5, 10, 14, 15, 22, 24], "ell_1": 0, "norm": 0, "sum_": [0, 12], "promot": 0, "sparsiti": [0, 9, 11], "solut": [0, 10, 14, 19], "lambda_": 0, "wx": 0, "multipli": [0, 11, 12, 14], "must": [0, 17, 18, 24, 25], "match": [0, 18, 20], "spars": [0, 9, 18], "through": [0, 14, 16, 17, 19, 20, 23], "sparsifi": 0, "w": [0, 14, 18], "chosen": [0, 11], "balanc": [0, 3, 18], "random": [0, 1, 6, 9, 18], "illustrat": 0, "diagram": [0, 5, 18], "below": [0, 1, 4, 5, 6, 10, 11, 12, 14, 16, 17, 19, 23, 24], "procedur": 0, "caption": 0, "figur": [0, 1, 2, 8, 10, 11, 12, 14, 19, 20, 23, 24], "http": [0, 1, 4, 5, 12, 13, 24], "doi": 0, "org": [0, 1, 12, 13], "10": [0, 7, 8, 10, 11, 14, 16, 18, 23], "1109": 0, "msp": 0, "2007": 0, "914728": 0, "heurist": 0, "A": [0, 1, 3, 5, 10, 12, 16, 17, 18, 19, 23, 24], "signal": [0, 1, 3, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 18, 19, 21, 23, 24], "8": [0, 2, 8, 10, 11, 12, 16, 19, 23, 24], "fold": [0, 1], "its": [0, 5, 7, 10, 11, 14, 18, 24], "d": [0, 5, 8, 9, 10, 14, 19, 20, 22], "b": [0, 9, 10, 12, 13, 15, 16, 24], "equispac": 0, "prevent": 0, "recoveri": [0, 9, 18], "incoher": [0, 1], "interfer": [0, 1, 16], "strong": [0, 11, 20, 24], "compon": [0, 1, 7, 14, 16, 18, 24], "stick": 0, "abov": [0, 7, 8, 11, 12, 14, 16, 18, 19, 20, 23, 24], "level": [0, 1, 9, 11], "recov": [0, 11, 24], "threshold": 0, "subtract": [0, 15, 16], "enabl": [0, 15, 18], "weaker": 0, "tv": 0, "tgv": 0, "wavelet": 0, "variabl": [0, 12], "densiti": [0, 9, 18, 20, 24], "preferenti": [0, 15, 18, 24], "difficult": 0, "thei": [0, 1, 3, 4, 7, 11, 15, 16, 17, 18, 19, 24], "inher": [0, 9], "denois": 0, "constrain": 0, "appar": [0, 22], "significantli": 0, "choic": [0, 11, 20], "most": [0, 3, 5, 7, 8, 9, 10, 11, 12, 14, 16, 17, 19, 23, 24], "common": [0, 3, 8, 9, 16, 23], "overfit": 0, "over": [0, 6, 8, 10, 13, 14, 16, 17, 20, 22], "smooth": 0, "unnatur": 0, "block": [0, 5, 17], "conceptu": 0, "train": [0, 3, 9, 18], "incorpor": [0, 12, 14, 20], "inform": [0, 1, 10, 11, 14, 17, 18, 20, 23, 24], "world": 0, "relev": [0, 12], "been": [0, 6, 11], "shown": [0, 5, 6, 10, 14, 16, 17, 19, 23, 24], "support": [0, 3, 9], "what": [0, 1, 2, 5, 7, 8, 10, 14, 15, 16, 17, 18, 24], "within": [0, 3, 9, 11, 17, 18, 19, 20, 22], "often": [0, 5, 11, 12, 14, 17, 20], "least": [0, 16, 18], "squar": [0, 20], "reg": 0, "implicitli": 0, "implement": [0, 19, 20], "via": [0, 7], "machin": 0, "attempt": [0, 7], "straightforward": 0, "approach": [0, 20], "cnn": 0, "invert": [0, 5], "after": [0, 3, 5, 8, 9, 10, 11, 15, 16, 17, 18, 24], "g_": [0, 8, 9, 18, 19], "dnn": 0, "neural": [0, 9], "network": [0, 9, 18, 21], "mani": [0, 1, 7, 11, 12, 14, 16, 17, 18, 21, 24], "weight": [0, 1, 3, 5, 9, 18, 20, 23], "prior": [0, 18, 22], "abl": [0, 24], "call": [0, 3, 4, 5, 8, 10, 11, 16, 19, 23, 24], "un": 0, "roll": 0, "becom": [0, 3, 14, 19, 22], "better": 0, "compact": 0, "design": [0, 7, 10, 15, 16, 20, 21], "mimic": 0, "classic": 0, "seri": 0, "cascad": 0, "modl": 0, "varnet": 0, "regularl": 0, "architectur": [0, 18], "gradient": [0, 1, 2, 6, 8, 9, 11, 13, 14, 18, 19, 20, 23], "updat": [0, 7, 10, 14, 23, 24], "descent": 0, "unet": [0, 18], "arxiv": 0, "ab": [0, 1, 2, 11, 12, 14, 19, 23], "2004": 0, "06688": 0, "e2": 0, "vn": 0, "take": [0, 4, 8, 11, 19, 20], "under": [0, 7, 10, 20, 24], "input": [0, 12], "ift": 0, "rss": 0, "bottom": [0, 4, 10, 16], "dc": 0, "modul": [0, 1, 14, 19, 20, 22], "bring": [0, 15], "intermedi": [0, 11, 19], "closer": [0, 24], "refin": 0, "map": [0, 1, 8, 9, 18, 21], "multi": [0, 9, 11, 18], "one": [0, 8, 10, 12, 14, 18, 20, 23, 24], "u": [0, 25], "net": [0, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 17, 18, 19, 21, 22, 24], "back": [0, 4, 10, 11, 14, 19, 23, 24], "sme": 0, "step": [0, 1, 8, 9, 18, 23, 24], "_w": 0, "structur": [0, 11, 13, 24], "overal": [0, 5, 7, 11, 14, 17, 20, 23], "similar": [0, 11, 12, 14], "both": [0, 3, 5, 8, 10, 17, 23, 24], "unrol": [0, 18], "lot": [0, 7], "4": [0, 1, 2, 7, 11, 12, 15, 16, 19, 20, 23], "radiolog": 0, "applic": [0, 7, 24], "question": [0, 15], "answer": [0, 15, 18], "qualiti": [0, 14, 20], "supervis": 0, "realist": 0, "modif": [0, 18, 20], "exist": 0, "increas": [0, 1, 3, 16, 18, 19, 20, 24], "size": [0, 1, 2, 5, 11, 12, 18, 20], "fastmri": 0, "provid": [0, 1, 8, 9, 11, 14, 16, 19, 20, 23], "thousand": 0, "high": [0, 1, 3, 9, 14, 16, 17], "med": 0, "nyu": 0, "edu": 0, "48550": 0, "1811": 0, "08839": 0, "resnet": 0, "possibl": [0, 16, 18, 20], "gpu": 0, "essenti": 0, "send": 0, "forward": 0, "compar": [0, 13, 18, 19, 20, 24], "output": [0, 12], "propag": 0, "choos": [0, 11, 20, 24], "l1": 0, "l2": 0, "batch": 0, "rate": [0, 1, 5, 10, 11, 13, 14, 17, 20, 23, 24], "etc": [0, 20], "challeng": [0, 7], "retain": 0, "textur": 0, "featur": [0, 10, 19, 21], "anatomi": [0, 16, 18], "might": 0, "eras": 0, "hallucin": 0, "although": [0, 4, 24], "physic": [0, 11, 20], "assur": 0, "recent": 0, "comprehens": [0, 1], "thes": 0, "reccommend": 0, "hammernik": 0, "k\u00fcstner": 0, "t": [0, 5, 6, 8, 9, 10, 12, 13, 14, 18, 19, 22, 23, 24], "yaman": 0, "huang": 0, "z": [0, 1, 4, 9, 10, 11, 13, 16, 17, 18, 19, 20, 23, 24], "rueckert": 0, "knoll": 0, "ak\u00e7akaya": 0, "driven": [0, 9], "medic": 0, "ieee": 0, "process": [0, 5, 7, 10, 12, 16, 21, 24], "mag": 0, "2023": [0, 7], "jan": 0, "40": [0, 11], "98": 0, "114": 0, "2022": 0, "3215288": 0, "epub": 0, "pmid": 0, "37304755": 0, "pmcid": 0, "pmc10249732": 0, "pdf": 0, "2203": 0, "12215": 0, "setup": [1, 2, 5, 6, 10, 11, 14, 15, 16, 19, 20, 23, 24, 25], "mri": [1, 2, 3, 5, 8, 10, 17, 19, 20, 23, 24], "educ": [1, 2, 5, 6, 10, 11, 14, 15, 16, 19, 20, 21, 23, 24], "resourc": [1, 2, 5, 6, 10, 11, 13, 14, 15, 16, 19, 20, 23, 24], "path": [1, 2, 5, 6, 10, 11, 14, 15, 16, 19, 20, 23, 24], "requir": [1, 2, 3, 4, 5, 6, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 23, 24], "cd": [1, 2, 5, 6, 10, 11, 14, 15, 16, 19, 20, 23, 24], "startup": [1, 2, 5, 6, 10, 11, 14, 15, 16, 19, 20, 23, 24], "notebook": [1, 21], "variou": [1, 3, 5, 7, 11, 16, 17, 19], "wikipedia": [1, 12], "en": [1, 12], "wiki": [1, 12], "mri_artifact": 1, "veri": [1, 6, 8, 10, 11, 14, 15, 17, 19, 20], "mitig": [1, 3, 5, 7, 14, 23], "them": [1, 3, 5, 7, 11, 14, 15, 16, 23, 24], "occur": [1, 10, 11, 14, 15, 18, 20, 24], "understood": 1, "perspect": 1, "particular": [1, 17], "equat": [1, 16, 18, 19, 22], "section": [1, 5, 8, 11, 22], "gener": [1, 3, 5, 8, 11, 13, 14, 18, 21, 22], "categor": 1, "tabl": [1, 16], "name": [1, 5, 8, 10, 19], "do": [1, 10, 11, 14, 15], "fov": [1, 9, 11, 15, 16], "too": 1, "small": [1, 11, 15, 16, 19, 21, 24], "parallel": [1, 8, 9, 18], "fail": 1, "swap": [1, 12], "pe": [1, 8, 9], "fe": [1, 18], "reacquir": 1, "gibb": [1, 14, 18], "ring": [1, 12, 14, 18, 19], "truncat": [1, 18], "due": [1, 5, 9, 11, 14, 15, 18, 20, 22], "fourier": [1, 8, 9, 11, 14, 18, 19, 22, 23], "edg": [1, 12, 14, 18], "rippl": [1, 19], "sharp": [1, 12, 19], "filter": [1, 14, 18, 23], "boundari": 1, "partial": [1, 6, 9, 18], "volum": [1, 9, 16, 22], "opposit": 1, "voxel": [1, 2, 3, 5, 9, 13, 18], "artifici": 1, "dark": [1, 18], "tissu": [1, 11, 14, 18, 19, 24], "fat": [1, 9, 14, 18, 23], "suppres": 1, "water": [1, 9, 14, 18, 23, 24], "dure": [1, 3, 5, 6, 7, 8, 9, 11, 15, 16, 17, 18, 19, 20, 22, 23], "copi": 1, "ghost": [1, 3, 18], "chang": [1, 2, 3, 4, 5, 9, 10, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "breath": 1, "gate": 1, "trigger": 1, "compens": 1, "suscept": [1, 3, 5, 9, 11, 14, 18, 21], "bandwidth": [1, 9, 18], "shim": 1, "suppress": [1, 9, 18, 23], "2dft": [1, 18], "epi": [1, 9, 14, 18, 23], "slice": [1, 9, 17, 18, 23], "3d": [1, 6, 8, 9, 24], "suscpet": 1, "implant": 1, "air": 1, "spin": [1, 4, 10, 11, 13, 14, 15, 16, 18, 19, 20], "echo": [1, 4, 8, 9, 11, 13, 14, 17, 18, 20, 23], "dielectr": 1, "shade": 1, "propog": 1, "unevenli": 1, "b1": [1, 4], "particularli": [1, 3, 14, 23], "larg": [1, 3, 5, 9, 15, 16, 19, 24], "b0": [1, 10, 16, 18], "insensit": [1, 4], "puls": [1, 7, 8, 11, 13, 14, 20, 21], "adiabat": 1, "bia": 1, "zipper": 1, "unwant": [1, 4], "noisi": 1, "top": [1, 10, 24], "shield": 1, "close": [1, 10, 14, 16, 23, 24], "door": 1, "check": [1, 4], "hardwar": [1, 15], "room": 1, "light": [1, 18], "At": [1, 18], "non": [1, 8, 10, 19, 24], "linear": [1, 6, 12, 14, 16, 19, 20, 22], "awai": [1, 10, 11, 16, 24], "isocent": 1, "subject": [1, 5, 10, 14, 15, 24], "warp": 1, "spike": 1, "intermitt": 1, "loos": 1, "connect": 1, "broken": [1, 5], "reli": [1, 3, 18], "unknown": 1, "disort": 1, "delta_": 1, "rbw": [1, 18], "fov_": [1, 2], "receiv": [1, 9, 13, 14, 15, 17, 18, 22], "view": [1, 8, 10, 11, 15, 18, 20], "accumul": [1, 5, 6, 8, 14, 22], "esp": [1, 3, 9], "adjac": [1, 11], "n_": [1, 8, 9, 18, 24], "To": [1, 5, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 24], "bw_": [1, 9, 18, 19], "ani": [1, 5, 7, 8, 10, 11, 14, 18, 20, 22, 24], "interleav": [1, 9], "without": [1, 10, 14], "acceler": [1, 3], "shot": [1, 3], "final": [1, 10, 14, 16], "select": [1, 9, 10, 11, 17, 18, 21, 23], "ss": [1, 9, 19], "inconsist": 1, "period": [1, 11, 19], "heart": 1, "beat": 1, "pulsatil": 1, "distinct": [1, 20], "sequenti": [1, 3, 18], "predict": [1, 9], "interv": 1, "60": [1, 11, 19], "per": [1, 9, 11], "minut": [1, 7], "irregular": 1, "arrhytthmia": 1, "cough": 1, "bulk": 1, "diffus": [1, 3, 14, 20, 21, 23], "datanam": 1, "se_t1_sag_data": 1, "kdata": [1, 2], "im_origin": 1, "ifft2c": [1, 2, 11, 14], "subplot": [1, 2, 8, 14, 16, 19, 20, 23], "121": [1, 8, 14, 20, 23], "imagesc": [1, 2, 11, 16, 23], "log": [1, 2], "max": [1, 2, 9, 20, 23], "colormap": [1, 2, 11, 16, 23], "grai": [1, 2, 11, 16, 23], "axi": [1, 2, 3, 4, 10, 11, 16, 18, 24], "tight": [1, 2, 11, 16], "122": [1, 8, 14, 20, 23], "warn": [1, 10, 14, 23, 24], "user": 1, "plarson": 1, "document": 1, "github": [1, 7], "mat": 1, "found": [1, 11], "search": 1, "n_undersamp": 1, "data_undersamp": 1, "zero": [1, 8, 10, 11, 19, 20, 23, 24], "iundersamp": 1, "round": [1, 16, 23], "im_undersamp": 1, "spike_loc": 1, "6": [1, 8, 10, 12, 19, 20, 23, 24], "53": 1, "data_spik": 1, "5": [1, 2, 8, 9, 10, 12, 14, 15, 16, 19, 20, 23, 24], "im_spik": 1, "rect": [1, 12], "32": [1, 12, 14], "kx": [1, 2, 8, 11, 12, 14, 18], "n_rect": [1, 2], "rect_ring": 1, "221": [1, 2, 19, 23], "222": [1, 2, 19], "ylabel": [1, 8, 10, 11, 14, 16, 19, 20, 23, 24], "kdata_window": 1, "ham": [1, 19], "rect_window": 1, "223": [1, 19, 23], "224": [1, 19], "window": [1, 10, 14, 19, 23, 24, 25], "relative_rf_frequ": 1, "ph_int": 1, "rand": 1, "rfint": 1, "data_rfint": 1, "repmat": [1, 14, 19], "im_rfint": 1, "amplitud": [1, 4, 8, 9, 11, 14, 16, 17, 18, 19, 24], "3": [1, 2, 8, 9, 10, 15, 16, 19, 20, 23, 24], "randn": 1, "imag": [2, 5, 7, 10, 12, 14, 15, 16, 17, 19, 20, 23, 24], "fundament": [2, 11, 24], "determin": [2, 12, 14, 15, 16, 17, 18, 19, 22, 23], "cell": [2, 8, 16], "syntaxerror": [2, 8, 16], "invalid": [2, 8, 16], "syntax": [2, 8, 16], "simpl": [2, 20], "base": [2, 6, 7, 9, 11, 12, 14, 16, 18, 19, 20, 22], "k_x": [2, 8, 12, 14, 18, 22], "rectangular": [2, 19], "demonstr": [2, 23], "256": [2, 11], "rect_recon": 2, "titl": [2, 8, 10, 11, 12, 14, 16, 19, 20, 23, 24], "kdata2": 2, "rect_recon2": 2, "doubl": 2, "kdata3": 2, "rect_recon3": 2, "tripl": 2, "One": [2, 4, 10, 16, 20, 24], "third": 2, "maximum": [2, 8, 9, 15, 16, 18, 20], "extent": [2, 16], "k_": [2, 9], "delta_x": [2, 18, 20], "symmetr": 2, "width": [2, 12], "w_k": 2, "kdata4": 2, "rect_recon4": 2, "4x": 2, "kdata8": 2, "7": [2, 16], "16": [2, 12], "9": [2, 10, 24], "rect_recon8": 2, "8x": 2, "modern": 3, "heavili": 3, "primarili": [3, 7, 9, 17], "method": [3, 5, 6, 8, 11, 17, 20, 21, 22], "acronym": [3, 5, 7], "contrast": [3, 5, 7, 10, 14, 17, 19, 24], "artifact": [3, 5, 7, 11, 12, 14, 16, 21, 23], "distort": [3, 9, 16, 18, 21], "t2": [3, 9, 10, 14, 18, 20, 21, 24], "blur": [3, 14, 18], "band": [3, 18], "bssfp": [3, 18], "refocus": [3, 4, 9, 11, 18, 19, 23], "exict": 3, "rapid": [3, 15], "relax": [3, 7, 9, 11, 13, 17, 18, 20, 22], "enhanc": [3, 14], "scanner": [3, 17, 18, 24], "ge": [3, 11, 18], "healthcar": 3, "turbo": 3, "siemen": 3, "healthin": 3, "tfe": [3, 8], "philip": 3, "clinic": [3, 18], "becaus": [3, 5, 10, 15, 18, 24], "highli": 3, "snr": [3, 9, 14], "effici": [3, 11, 18], "effect": [3, 4, 8, 9, 11, 12, 14, 20], "pd": [3, 9], "length": [3, 8, 9, 10, 11, 16, 19, 20, 23, 24], "etl": [3, 9], "repetit": [3, 11, 17, 18], "te": [3, 5, 9, 14, 17, 18, 20], "te_": [3, 9, 11], "eff": [3, 9], "closest": [3, 9, 16], "pro": 3, "con": 3, "sar": [3, 9, 18, 19], "repeat": [3, 5, 8, 9, 11, 15, 17, 18, 23, 24], "commonli": [3, 11, 12, 15, 18], "fmri": [3, 23], "extrem": [3, 12, 20, 24], "displac": [3, 18, 23], "fidel": 3, "nyquist": [3, 18], "basic": [3, 4, 11, 12, 17, 21], "befor": [3, 8, 11, 18, 19], "next": [3, 8, 18], "unbalanc": 3, "dephas": [3, 5, 8, 9, 11, 18], "elimin": [3, 5, 9, 11, 18, 23], "truli": 3, "rotat": [3, 4, 8, 9, 14, 16, 17, 18, 19, 24], "everi": [3, 5, 11, 16, 17, 18, 20], "chanc": 3, "previou": 3, "coher": 3, "excit": [3, 5, 8, 9, 11, 13, 15, 18, 22, 23], "scheme": [3, 11], "quadrat": 3, "increment": [3, 8], "spgr": 3, "angl": [3, 4, 5, 9, 16, 17, 18, 20, 24], "flash": 3, "aim": [3, 19, 23], "pure": [3, 5], "t1": [3, 9, 10, 18, 20, 21, 24], "recal": [3, 5, 6], "steadi": [3, 11, 18], "grass": 3, "precess": [3, 5, 9, 14, 16, 18, 22], "fisp": 3, "residu": [3, 14], "refouc": 3, "free": [3, 18], "ssfp": [3, 14], "revers": [3, 5, 12, 22], "psif": 3, "refocu": [3, 5, 18], "later": [3, 11, 14, 16, 17, 24], "truefisp": 3, "No": [3, 5], "preserv": 3, "ye": 4, "you": [4, 5, 7, 10, 11, 13, 24], "heard": 4, "me": 4, "mayb": 4, "type": [4, 5, 7, 8, 11, 13, 14, 15, 17, 18, 19, 20], "person": 4, "think": 4, "out": [4, 5, 6, 8, 9, 11, 13, 14, 18, 20], "interest": [4, 16, 20], "movi": [4, 8], "spinbench": [4, 7], "heartvista": 4, "ai": 4, "class": [4, 5, 11], "b_1": [4, 9, 13, 19, 23, 24], "inhomongen": 4, "similarli": [4, 12, 20], "even": 4, "transmit": [4, 9, 13, 15, 18], "mostli": 4, "180": [4, 5, 10, 11, 18, 19, 20], "degre": [4, 5, 10, 18, 19, 20], "flip": [4, 5, 9, 16, 17, 18, 20, 23], "purpos": [4, 15, 16, 17, 19, 21], "show": [4, 6, 8, 10, 11, 12, 14, 16, 17, 19], "two": [4, 5, 20, 23, 24], "sweep": 4, "again": [4, 10, 14, 24], "second": [4, 11, 17], "yellow": 4, "white": [4, 11], "rang": [4, 7, 11, 15, 16, 18, 19, 21], "around": [4, 10, 11, 15, 16, 17, 19, 24], "larmor": [4, 10, 11, 16, 17, 18, 19, 24], "plot": [4, 8, 10, 11, 12, 14, 16, 19, 20, 23, 24], "corner": 4, "continu": [4, 12, 24], "constant": [4, 5, 8, 9, 11, 18, 19, 22, 24], "hard": [4, 5, 10, 18], "frequneci": [4, 14, 22], "broad": [5, 7], "simpler": 5, "undesir": [5, 11], "build": [5, 14, 19, 21, 25], "g_x": [5, 8, 13, 18], "cancel": 5, "anoth": [5, 11, 19, 24], "And": [5, 14, 16, 20, 24], "simplifi": [5, 10, 14, 22, 24], "exhibit": 5, "explain": [5, 7, 10], "propto": [5, 9, 11, 19, 20], "m_0": [5, 9, 10, 11, 13, 18, 20, 24], "ideal": [5, 11, 12, 17], "uniform": 5, "absens": [5, 24], "unavoid": 5, "refer": [5, 8, 10, 15, 19, 24], "f_r": [5, 11, 14], "bar": [5, 8, 9, 10, 11, 13, 14, 15, 16, 19, 22, 24], "gamma": [5, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 22, 23, 24], "imperfect": [5, 14], "decai": [5, 11, 18, 24], "smallest": 5, "sum": [5, 9, 14, 19, 22, 23, 24], "int_": [5, 12, 20, 22], "approx": [5, 11, 16, 22, 24], "note": [5, 6, 7, 8, 11, 12, 14, 16, 17, 18, 19, 20], "reconstruct": [5, 8, 9, 11, 12, 14, 21, 22], "mechan": [5, 11], "de": 5, "averag": [5, 20], "magnitud": [5, 16, 18, 19], "illustr": [5, 6, 8, 10, 11, 12, 19, 21, 24], "t2star_spinecho_illustr": 5, "80": [5, 10, 11, 24], "ms": [5, 10, 11, 14, 16, 19, 20, 23], "mild": 5, "approxim": [5, 9, 11, 18, 19, 20, 23], "up": [5, 7, 10, 11, 14, 16, 18, 19, 24], "separ": [5, 9, 11, 14, 15, 16, 18, 23, 24], "leq": [5, 11], "easili": [5, 20, 23], "doe": [5, 9, 14, 18, 20, 25], "make": [5, 15], "revert": 5, "try": [5, 10, 12], "visit": 5, "drcmr": [5, 24], "dk": [5, 24], "blochsimul": 5, "scene": [5, 10], "90x": [5, 10], "180y": 5, "happen": [5, 18, 19], "180x": 5, "Is": 5, "still": [5, 12], "multipl": [5, 9, 11, 12, 17, 18, 19], "order": [5, 6, 11, 22, 23, 24], "give": [5, 15, 16, 18], "collect": [6, 18], "cartesian": [6, 14], "done": [6, 11, 14, 17, 20, 23, 24], "anticip": 6, "formul": [6, 9, 12, 14, 22, 23, 24], "introduc": [6, 11, 17, 19, 22, 24], "proport": [6, 8, 9, 11, 16, 18, 19, 20, 22, 24], "s_i": 6, "denot": [6, 12, 14, 16], "subscript": 6, "trajectori": [6, 9, 14, 22, 23], "raster": [6, 8], "fashion": [6, 17], "knowledg": [6, 14], "mr": [6, 11, 13, 16, 20, 22, 23, 24], "store": [6, 18, 22], "onc": [6, 7, 8, 11, 14, 20, 24], "simpli": [6, 12, 14, 15, 16, 24], "fast": [6, 12, 14], "fft": [6, 12, 19], "anim": [6, 7, 10, 19], "short": [7, 9, 11, 19], "book": [7, 13, 25], "associ": [7, 10, 18, 19], "larsonlab": 7, "repositori": 7, "helper": [7, 11], "built": 7, "about": [7, 17, 19, 24], "decad": 7, "teach": 7, "1st": 7, "year": 7, "graduat": 7, "student": 7, "background": [7, 16], "natur": [7, 11], "scienc": 7, "engin": 7, "undergo": 7, "fall": 7, "quarter": 7, "promin": 7, "role": 7, "my": [7, 21], "upon": 7, "should": [7, 10, 16, 19, 20, 23, 24], "achiev": [7, 10, 11, 15, 18, 19, 24], "fundmanet": [7, 15, 16], "why": [7, 9, 15, 16, 22], "necessari": [7, 12, 15, 16, 17, 19], "concept": [7, 10, 14, 18, 21, 22, 24], "polar": [7, 9, 10, 13, 15, 16, 18, 22], "jump": 7, "pretti": 7, "quickli": [7, 19], "quick": 7, "overview": 7, "access": 7, "playlist": 7, "record": [7, 17], "goe": [7, 19], "avail": [7, 9, 10, 19, 21, 24], "git": 7, "icon": 7, "recommend": [7, 10, 14, 23, 24], "clone": 7, "desktop": 7, "wai": [7, 8, 11, 16, 17, 18], "pull": 7, "made": [7, 10, 14, 23, 24], "greatli": [7, 10, 14], "influenc": [7, 10, 14, 20], "great": 7, "want": 7, "front": 7, "dwight": 7, "nishimura": 7, "text": 7, "borrow": 7, "materi": [7, 11, 15], "own": [7, 14], "bill": 7, "tool": [7, 12, 17, 21], "miki": 7, "lustig": 7, "danish": 7, "research": 7, "centr": 7, "bloch": [7, 14, 18, 19, 24], "By": [8, 11, 16], "far": [8, 16], "fact": 8, "regularli": 8, "turn": [8, 9, 10, 16, 17, 18, 22, 24], "read": [8, 17, 18, 20], "present": [8, 10, 11, 12, 16], "given": [8, 9, 11, 18, 19, 24], "convent": [8, 16, 24], "xr": [8, 9, 18], "therefor": [8, 11, 15, 20, 24], "posit": [8, 9, 16, 18, 19, 22, 23], "alon": [8, 20], "1d": 8, "mxy": [8, 18], "ones": [8, 10, 11, 12, 19, 23], "meshgrid": [8, 11, 14, 19], "splot": 8, "kfe": 8, "dt": [8, 10, 11, 14, 19, 23], "42": [8, 10, 14, 19, 23, 24], "58": [8, 10, 14, 19, 23], "linspac": [8, 10, 11, 12, 16, 19, 20, 23, 24], "phase_x": 8, "mxy_f": [8, 23], "05": [8, 16], "quiver": [8, 16], "xlabel": [8, 10, 11, 12, 14, 16, 19, 20, 23, 24], "xlim": [8, 19], "ylim": [8, 20], "drawnow": 8, "2nd": [8, 11], "option": [8, 10], "3rd": 8, "phi": [8, 9, 12], "yp": [8, 16], "yi": [8, 9], "t_y": [8, 9], "strength": [8, 9, 10, 16, 18, 20], "durat": [8, 10, 14, 18, 19, 20], "equival": [8, 19, 20], "kpe": 8, "tpe": 8, "ip": 8, "phase_i": 8, "mxy_p": 8, "g_y": [8, 13, 18], "int2str": [8, 11, 14, 19, 20], "instead": [8, 10, 14, 23, 24], "visual": [8, 10, 19, 24], "see": [8, 9, 10, 11, 14, 15, 17, 20, 22, 24], "spatial_encoding_mxy_illustr": 8, "code": [8, 10, 21, 23], "int_0": [8, 9, 14, 19, 20, 22], "tau": [8, 9, 12, 14, 18, 19, 20, 22], "alwai": [8, 11, 15, 16, 18, 24], "start": [8, 10, 12, 14, 15, 18, 22, 24], "initi": [8, 11, 14, 22], "neg": 8, "experi": [8, 10, 11, 14, 16, 17, 20, 22, 24], "radial": [8, 14], "spiral": [8, 14], "planar": [8, 14, 18, 23], "blade": 8, "ky": [8, 11, 14], "linewidth": [8, 12], "k_y": [8, 12, 14, 18, 22], "kx_ep": 8, "ky_ep": 8, "k_theta": 8, "k_radial": 8, "201": [8, 23], "nturn": 8, "k_spiral": 8, "kz": 8, "plot3": [8, 23], "reshap": [8, 14], "zlim": 8, "zlabel": [8, 11], "k_z": [8, 22, 23], "n_radial": 8, "co": [8, 9, 10, 11, 12, 16, 18, 20], "asin": 8, "sin": [8, 9, 10, 11, 12, 16, 20], "math": [9, 10], "electr": [9, 15, 16], "nuclear": [9, 15, 16], "equilibrium": [9, 10, 11, 13, 15, 16], "i_z": [9, 24], "bmatrix": [9, 10, 13, 16, 24], "static": [9, 18], "m_z": [9, 10, 11, 13, 18, 19, 24], "radiofrequ": 9, "homogen": [9, 15, 16], "proton": [9, 18, 20, 23, 24], "spoil": [9, 18, 20], "gre": [9, 18, 20], "theta": [9, 10, 11, 17, 18, 19, 20], "ernst": [9, 11, 20], "theta_": [9, 11, 20], "prepar": [9, 18], "ir": [9, 11], "ti": [9, 11, 18], "iron": [9, 11, 15], "oxygen": [9, 11], "versu": [9, 11, 14], "deoxygen": [9, 11], "blood": [9, 11], "chemcial": 9, "environ": [9, 11, 25], "atom": [9, 11, 24], "local": [9, 11, 22], "consider": 9, "ppm": [9, 11, 16], "intra": 9, "spectral": 9, "agent": 9, "gadolinium": [9, 11], "gd": [9, 11], "shorten": [9, 11], "shape": [9, 17, 23], "product": 9, "tbw": [9, 19, 23], "thick": 9, "f_": [9, 11, 14, 19, 20], "z_": [9, 19], "wise": 9, "cumul": [9, 22], "area": [9, 11, 12, 18, 20, 22], "seq": [9, 20], "mea": [9, 20], "resolut": [9, 23], "rel": [9, 11, 12, 15, 16, 17, 20], "volumetr": 9, "coverag": 9, "multislic": [9, 18], "fse": 9, "tse": 9, "rare": 9, "subsequ": 9, "mai": [9, 18], "autocalibr": 9, "compress": [9, 18, 21], "sens": [9, 18, 21], "coeffici": [9, 12, 20], "deep": [9, 18], "learn": [9, 18], "dataset": [9, 18], "comparison": 9, "physicist": 10, "felix": 10, "who": 10, "won": 10, "nobel": 10, "prize": 10, "discoveri": 10, "phenomena": 10, "almost": 10, "behavior": [10, 14, 17, 19], "seen": [10, 11], "deriv": [10, 12, 14, 24], "kei": [10, 14, 16, 19], "interact": [10, 11, 14, 15, 18, 23, 24], "gnuplot": [10, 14, 23, 24], "graphic": [10, 14, 23, 24], "toolkit": [10, 14, 23, 24], "discourag": [10, 14, 23, 24], "activ": [10, 14, 16, 17, 23, 24, 25], "maintain": [10, 14, 23, 24], "limit": [10, 11, 12, 14, 18, 19, 20, 23, 24], "ulik": [10, 14, 23, 24], "fix": [10, 11, 14, 19, 23, 24], "commun": [10, 14, 23, 24], "pipe": [10, 14, 23, 24], "pass": [10, 14, 23, 24], "octav": [10, 14, 23, 24], "interpret": [10, 14, 23, 24], "reflect": [10, 11, 14, 23, 24], "manag": [10, 14, 23, 24], "mous": [10, 14, 23, 24], "click": [10, 14, 23, 24], "notifi": [10, 14, 23, 24], "intern": [10, 11, 14, 23, 24], "list": [10, 13, 14, 23, 24], "open": [10, 14, 15, 17, 23, 24], "qt": [10, 14, 23, 24], "respons": [10, 14, 19], "vast": 10, "major": [10, 11, 19, 20], "beavhior": 10, "longitudin": [10, 11, 18, 24], "lattic": [10, 11, 18, 24], "valuabl": [10, 24], "onlin": 10, "hand": [10, 16], "observ": [10, 12, 24], "neglect": [10, 14, 18, 22], "rightarrow": [10, 12], "infti": [10, 12, 22], "thin": 10, "5e3": 10, "1500": [10, 11], "mt": [10, 14, 16, 19], "unit": [10, 11, 13, 16, 19], "bloch_rot": [10, 19], "mstart": 10, "bstatic": 10, "1e": [10, 16], "ns": 10, "300": 10, "mall": [10, 24], "legend": [10, 11, 19, 20, 23, 24], "north": [10, 24], "boxoff": [10, 24], "5540": [10, 24], "oscil": [10, 16, 18, 23, 24], "orthogon": 10, "b_": [10, 16, 18], "energi": [10, 11, 15, 16, 19, 23, 24], "good": [10, 11, 13, 19], "progress": 10, "simplif": [10, 22], "f_0": [10, 11, 14, 16, 24], "stationari": 10, "represent": [10, 17, 18, 22], "now": [10, 14, 19, 22, 23, 24], "analysi": [10, 14], "45": [10, 18], "90": [10, 18, 19, 20], "default": [10, 24], "Then": [10, 11, 14, 23], "button": [10, 24], "go": 10, "creation": [10, 15], "gammabar": [10, 14, 19], "khz": [10, 14, 16, 18, 19], "simplic": [10, 14], "f0": [10, 19], "m0": [10, 11, 19, 20, 24], "m_equilibrium": [10, 19], "paaramet": 10, "t_rf": 10, "4000": [10, 11], "rf_flip_angl": 10, "radian": [10, 18], "b10": [10, 19], "425": 10, "8713e": 10, "03": 10, "12": [10, 16, 18, 23], "513": 10, "omega_0": 10, "northwest": 10, "192": 10, "clearli": 10, "438": 10, "equilibriuam": 10, "ultim": [10, 15], "orient": [10, 16, 24], "same": [10, 11, 14, 16, 18, 19], "shorthand": [10, 13], "complex": [10, 11, 13, 14], "adjust": [10, 24], "situat": [10, 14, 18], "millitesla": [10, 16], "tip": [10, 13, 17, 19, 24], "m_start": [10, 24], "bloch_rftip": 10, "bloch_relax": [10, 24], "1232e": 10, "17": 10, "0000e": 10, "00": 10, "num2str": [10, 11, 12, 16, 20], "657": 10, "rich": 11, "varieti": 11, "arguabl": [11, 19], "advantag": [11, 18, 19], "desir": [11, 19, 20], "intrins": 11, "molecular": 11, "signific": [11, 17], "precis": [11, 19], "quantum": 11, "human": [11, 18, 24], "divid": [11, 14, 16, 24], "liquid": [11, 15], "fluid": 11, "solid": 11, "cortic": 11, "bone": 11, "tendon": 11, "fibrosi": 11, "proteinac": 11, "organ": 11, "exchang": 11, "surround": [11, 16], "motion": [11, 18], "characterist": [11, 20], "transfer": [11, 21], "longer": [11, 18, 20], "lipid": [11, 23, 24], "shorter": [11, 14, 18, 20], "edema": 11, "lose": 11, "freedom": 11, "macromolecul": 11, "coupl": [11, 13], "stronger": [11, 15, 16], "microscop": 11, "molecul": [11, 23], "macroscop": 11, "cannot": [11, 18, 24], "caus": [11, 15, 19, 24], "import": [11, 17, 19, 20], "deposit": [11, 15, 23], "presenc": [11, 19], "calcif": 11, "calcium": 11, "vs": [11, 19], "hemoglobin": 11, "vein": 11, "basi": [11, 22, 24], "bold": 11, "brain": 11, "matter": 11, "790": 11, "920": 11, "100": [11, 14, 15, 16, 18, 19], "cerebrospin": 11, "csf": 11, "2000": 11, "arteri": 11, "1200": 11, "50": [11, 16], "liver": 11, "parenchyma": 11, "490": 11, "lung": 11, "830": 11, "myocardium": 11, "870": 11, "skelet": 11, "muscl": 11, "260": 11, "handbook": 11, "800": [11, 20], "110": 11, "1300": 11, "3700": 11, "1700": 11, "1000": [11, 18], "30": 11, "400": [11, 20], "cartilag": 11, "pictur": 11, "control": [11, 19, 20], "se": [11, 18], "200": 11, "t2v": 11, "130": 11, "s_te": 11, "150": 11, "mesh": [11, 14], "155": 11, "colorbar": [11, 16, 23], "incomplet": 11, "simplest": 11, "reach": 11, "acqrui": 11, "maxim": 11, "evolut": 11, "ntr": 11, "500": [11, 23], "nt_per_tr": 11, "t_per_tr": 11, "t_minu": 11, "t_plu": 11, "mz_minu": 11, "mz_plu": 11, "ep": [11, 19], "mz_all": 11, "o": 11, "t1v": 11, "s_tr": 11, "2500": 11, "s_flip": 11, "Not": 11, "enough": [11, 15, 17], "amount": [11, 12, 17, 19], "therebi": 11, "discuss": [11, 16], "principl": [11, 14, 16], "smaller": [11, 16], "boost": 11, "leav": 11, "certain": [11, 15], "ratio": [11, 13, 16, 24], "zoom": 11, "delai": 11, "strategi": [11, 14], "null": 11, "stir": 11, "attenu": 11, "flair": 11, "flip1": 11, "flip2": 11, "750": 11, "mz1_minu": 11, "mz2_minu": 11, "mz1_plu": 11, "mz2_plu": 11, "t1_minu": 11, "t1_plu": 11, "t2_minu": 11, "t2_plu": 11, "evolv": [11, 23], "find": [11, 12, 23], "2001": 11, "4001": 11, "6001": 11, "751": 11, "2751": 11, "4751": 11, "s_ti": 11, "chelat": 11, "superparamagnet": 11, "oxid": 11, "wherev": 11, "quantifi": 11, "r_1": 11, "r_2": 11, "typiclali": 11, "l": [11, 12], "mmol": 11, "cm": [11, 16, 23], "concentr": 11, "mm": 11, "hydrogen": [11, 24], "exploit": 11, "isol": [11, 16], "model": [11, 12], "peak": [11, 14, 19], "part": [11, 24], "million": 11, "220": 11, "hz": [11, 13, 14, 16, 18, 23, 24], "440": 11, "dixon": [11, 18], "realiti": [11, 17], "account": [11, 19, 20], "fatti": 11, "three": [11, 20], "circular": 11, "jinc": 11, "circl": 11, "circ": 11, "k_r": 11, "signal_gr": 11, "mrsignal_spoiled_gradient_echo": [11, 20], "contrast_phantom": 11, "nphan": 11, "xc": 11, "yc": 11, "25": 11, "1e3": [11, 14, 23], "06": 11, "64": [11, 12, 16], "ball": 11, "radiu": [11, 16], "20": [11, 19, 23], "160": 11, "3000": 11, "coordin": 11, "ad": [11, 17, 18, 19], "togeth": [11, 16, 19, 20], "individu": [11, 14, 16, 24], "exponenti": [11, 24], "displai": 11, "tan": 12, "funcion": 12, "ne": 12, "dx": 12, "ax": [12, 17], "ast": 12, "dirac": 12, "comb": 12, "sha": 12, "\u0448": 12, "rectangl": [12, 17], "sqcap": 12, "quad": 12, "normal": [12, 20], "intuit": [12, 14], "slid": 12, "nice": [12, 21], "unitari": 12, "ordinari": 12, "dk_x": 12, "dy": 12, "f_x": 12, "f_y": 12, "finit": 12, "kspace": 12, "w_": [12, 18], "accord": [12, 18], "convolv": [12, 14], "notabl": 12, "decomposit": 12, "512": 12, "kxmax": 12, "128": 12, "kxmax_trunc": 12, "fftshift": [12, 19], "ifft": 12, "ifftshift": 12, "power": [12, 14, 15, 16, 18, 19, 20, 21, 22], "actual": [12, 17], "dft": 12, "x_n": 12, "k_n": 12, "formula": 12, "extend": [12, 20], "si": 13, "gyromagnet": [13, 16, 24], "g_z": [13, 18, 23], "b_x": [13, 16], "b_y": [13, 16], "b_z": [13, 16, 22], "jargon": 13, "intimid": [13, 14], "imped": 13, "luckili": 13, "radiopaedia": 13, "articl": 13, "abbrevi": 13, "vendor": 13, "com": 13, "serv1": 13, "php": 13, "cam": 13, "format": 14, "equiat": 14, "impact": [14, 20], "affect": [14, 20], "resonnac": 14, "obtain": 14, "int": 14, "reason": [14, 20], "clear": 14, "soon": [14, 22], "add": [14, 15, 16, 23], "easiest": 14, "c_n": 14, "s_n": 14, "receiev": 14, "integr": [14, 19, 20, 22], "upsilon": 14, "gxr": [14, 18], "kx0": 14, "upsilon_cartesian": 14, "tesp": 14, "dky": 14, "deadtim": 14, "tall": 14, "upsilon_epi": 14, "corrupt": 14, "convolut": 14, "w_cartesian": 14, "w_epi": 14, "x0": 14, "height": 14, "outsid": [14, 19], "get": [14, 17, 24], "wors": 14, "speci": 14, "examin": [14, 20], "could": 14, "index": 14, "complic": 14, "gain": [14, 18, 20], "look": [14, 15, 17, 18, 19, 24], "_0": [14, 22], "r_0": 14, "star": 14, "df": [14, 19, 23], "frfom": 14, "side": [14, 16, 20], "lobe": 14, "interpol": [14, 20], "write": 14, "version": [14, 23], "numer": [14, 20], "solver": 14, "graph": 14, "As": [14, 19, 24], "framework": [14, 22], "express": 14, "spread": [14, 19], "psf": 14, "impuls": 14, "boil": 14, "down": [14, 19, 24], "decompos": [14, 20], "m_i": 14, "w_i": 14, "sum_i": 14, "m_1": 14, "m_2": 14, "w_1": 14, "w_2": 14, "accur": 14, "thw": 14, "flow": [14, 22], "explor": 15, "deconstruct": 15, "insid": 15, "insight": 15, "loud": 15, "danger": 15, "metal": 15, "cut": 15, "greater": 15, "tesla": 15, "manget": [15, 24], "superconduct": 15, "alloi": 15, "bath": 15, "helium": 15, "dager": 15, "ferromagnet": [15, 18], "suck": 15, "antenna": 15, "electromagnet": [15, 16, 24], "perturb": [15, 16, 24], "releas": 15, "radio": [15, 16], "mhz": [15, 16, 18], "excitaiton": [15, 18], "thermal": [15, 24], "linearli": [15, 20, 22], "switch": [15, 16, 17, 19, 24], "current": 15, "exert": 15, "forc": 15, "lorentz": 15, "vibrat": 15, "place": [15, 16, 18, 24], "fiel": 15, "distinguish": 15, "critic": [16, 20], "summar": [16, 20], "mu": [16, 18, 24], "wire": 16, "govern": [16, 24], "maxwel": 16, "rule": 16, "link": 16, "solenoid": 16, "ensur": 16, "usual": [16, 17, 18], "never": 16, "perfect": 16, "ll": 16, "few": [16, 19, 21], "Their": 16, "00001": 16, "perpedicularli": 16, "plane": [16, 17, 18], "reactiv": 16, "capacitor": 16, "inductor": 16, "kw": 16, "mv": 16, "aris": [16, 18], "channel": 16, "put": [16, 20, 22], "i0": 16, "amp": 16, "mu0": 16, "401": 16, "bz": 16, "211": [16, 19, 23], "212": [16, 19, 23], "resons": 16, "event": 16, "amplifi": 16, "digit": 16, "tell": 16, "birdcag": 16, "perpendicular": [16, 18, 24], "tailor": 16, "knee": 16, "abdomen": 16, "head": 16, "configur": [16, 18], "decoupl": 16, "detun": 16, "don": 16, "senit": 16, "move": [16, 18, 24], "brightest": 16, "biot": 16, "savart": 16, "law": 16, "flag_2d": 16, "just": [16, 21], "bx": 16, "BY": 16, "xp": 16, "zp": 16, "loop_coil_field": 16, "18": 16, "bmag": 16, "xhalf": 16, "chapter": [17, 24], "indic": 17, "conjunct": 17, "remeb": 17, "incred": [17, 22], "convei": 17, "experiment": 17, "speed": 17, "drawn": 17, "bracket": 17, "simlifi": 17, "crusher": 17, "destruct": 17, "instantan": 17, "slew": [17, 23], "trapezoid": 17, "3t": 18, "5t": 18, "xrai": 18, "visibl": 18, "fm": 18, "am": 18, "proper": 18, "assign": 18, "conduct": 18, "isotop": 18, "1h": 18, "13": [18, 24], "19": [18, 24], "2h": 18, "diamagnet": 18, "paramagnet": 18, "immedi": 18, "equilibirum": 18, "lab": [18, 19], "frame": [18, 19], "flux": 18, "benefit": 18, "doesn": 18, "contribut": [18, 24], "highest": 18, "2e": 18, "pdw": 18, "t1w": 18, "t2w": 18, "additoin": 18, "daq": 18, "serv": 18, "statement": 18, "true": 18, "overlap": 18, "prewind": 18, "\u03b8": 18, "twice": 18, "thinner": 18, "decreas": 18, "bw": [18, 19], "theorem": 18, "avoid": 18, "lowest": 18, "oversampl": 18, "3dft": 18, "anti": 18, "fov_x": 18, "none": 18, "stretch": [18, 19], "pile": 18, "bright": 18, "rapidli": 18, "robust": 18, "intravoxel": 18, "gather": 18, "databas": 18, "outer": 18, "amplif": 18, "acquist": 18, "Of": 18, "regardless": 18, "develop": 18, "000": 18, "decod": 18, "recurr": 18, "appl": 19, "detail": 19, "distanc": 19, "absorb": 19, "heat": 19, "safeti": 19, "minim": 19, "sinusoid": 19, "002": 19, "tmax": 19, "rf_sinusoid": 19, "ft_sinusoid": 19, "imaginari": 19, "tmat": 19, "dfmat": 19, "rf_all": 19, "rf_n": 19, "ft_n": 19, "fwidth": 19, "11": [19, 23], "rf_sinc": 19, "ft_sinc": 19, "gz": [19, 23], "poorli": 19, "uniformli": 19, "forth": [19, 24], "substanti": 19, "meanwhil": 19, "wide": [19, 20], "wherea": [19, 24], "360": 19, "address": 19, "impli": [19, 20], "shrunk": 19, "bwplot": 19, "IN": 19, "rf_shape": 19, "trf": 19, "bwrf": 19, "plai": 19, "notic": [19, 24], "sharper": 19, "But": [19, 20], "break": 19, "sophist": 19, "shinnar": 19, "le": 19, "roux": 19, "slr": 19, "dzrf": [19, 23], "isn": 19, "issu": 19, "themselv": 19, "subtli": 19, "degrad": 19, "inv": 19, "theoret": 20, "foundat": 20, "delta_i": 20, "delta_z": 20, "gaussian": 20, "root": 20, "sigma": 20, "downtim": 20, "intrigu": 20, "trdt1": 20, "01": 20, "1600": 20, "inf": 20, "theta_optim": 20, "snr_effici": 20, "it1": 20, "aco": 20, "drop": 20, "stabl": 20, "finer": 20, "coarser": 20, "nativ": 20, "pad": 20, "nearbi": 20, "scale": [20, 23], "care": 20, "taken": 20, "demonin": 20, "tread": 20, "snr_t2s_onesid": 20, "imax_onesid": 20, "snr_t2s_twosid": 20, "imax_twosid": 20, "disp": 20, "2806": 20, "4907": 20, "ve": 21, "favorit": 21, "focus": 21, "kmjohnson3": 21, "intro": 21, "python": 21, "jupyt": [21, 25], "introduct": 21, "mribri999": 21, "mrsignalsseq": 21, "cours": 21, "lectur": 21, "introductori": 21, "marku": 21, "nilsson": 21, "matlab": 21, "mikgroup": 21, "sigpi": 21, "packag": 21, "mrirecon": 21, "bart": 21, "toolbox": 21, "qmrlab": 21, "quantit": 21, "fit": 21, "ismrm": 21, "mrhub": 21, "hub": 21, "worth": 21, "brows": 21, "delv": [21, 24], "topic": 21, "sort": 22, "stop": 22, "undo": 22, "motiv": 22, "rather": 22, "textrm": 22, "i2": 22, "amaz": 22, "appropri": 22, "spectroscopi": 23, "relat": 23, "reveal": 23, "travers": 23, "psace": 23, "trick": 23, "compil": 23, "abr": 23, "mex": 23, "file": 23, "error": 23, "re": 23, "run": 23, "abrx": 23, "31": [23, 24], "column": 23, "trajectoi": 23, "nlobe": 23, "nspec": 23, "nramp": 23, "ramp": 23, "g1": 23, "gamp": 23, "95": 23, "mod": 23, "nrw": 23, "grw": 23, "cumsum": 23, "k_f": 23, "h_f": 23, "h_z": 23, "envelop": 23, "subpuls": 23, "4258": 23, "slewmax": 23, "15e3": 23, "gmax": 23, "20e": 23, "sbw": 23, "dz": 23, "10e": 23, "verse_frac": 23, "nspat": 23, "nwait": 23, "rfspec": 23, "gf": 23, "ab2ex": 23, "g_f": 23, "rfspat": 23, "min": 23, "ceil": 23, "floor": 23, "vers": 23, "rfspatv": 23, "isnan": 23, "g1z": 23, "mxy_z": 23, "flip_scal": 23, "rfscaleg": 23, "589": 23, "mxy_2d": 23, "m_xy": 23, "watch": 23, "behav": 24, "phenomenom": 24, "nucleu": 24, "angular": 24, "momentum": 24, "moment": 24, "act": 24, "respond": 24, "tyipcal": 24, "nuclei": 24, "primari": 24, "23": 24, "na": 24, "p": 24, "abund": 24, "absenc": 24, "randomli": 24, "ensembl": 24, "arrow": 24, "vertic": 24, "www": 24, "planck": 24, "63e": 24, "34": 24, "58e6": 24, "boltzmann": 24, "62e": 24, "ev": 24, "38e": 24, "temperatur": 24, "310": 24, "prefer": 24, "boltzman": 24, "uparrow": 24, "downarrow": 24, "kt": 24, "expon": 24, "strongli": 24, "analog": 24, "swing": 24, "your": 24, "leg": 24, "wrong": 24, "compassmr": 24, "compass": 24, "mode": 24, "slider": 24, "freq": 24, "uenci": 24, "new": 24, "checkbox": 24, "hit": 24, "push": 24, "needl": 24, "blue": 24, "trace": 24, "highlight": 24, "composit": 24, "last": 24, "mx": 24, "anaconda": 25, "prompt": 25, "FOR": 25, "conda": 25, "wintest": 25, "pip": 25, "instal": 25, "forg": 25, "octave_kernel": 25, "jb": 25, "booknam": 25, "runjb": 25, "quantecon": 25, "mini": 25, "seem": 25}, "objects": {}, "objtypes": {}, "objnames": {}, "titleterms": {"acceler": [0, 9, 18], "imag": [0, 1, 3, 6, 8, 9, 11, 18, 22], "method": [0, 9, 18], "learn": [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14, 15, 16, 17, 19, 20, 22, 23, 24], "goal": [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14, 15, 16, 17, 19, 20, 22, 23, 24], "gener": 0, "formul": 0, "mri": [0, 6, 7, 9, 11, 12, 13, 14, 15, 16, 18, 21, 22], "reconstruct": [0, 6, 18], "partial": 0, "fourier": [0, 6, 12], "parallel": 0, "model": 0, "base": 0, "linear": 0, "predict": 0, "snr": [0, 18, 20], "artifact": [0, 1, 9, 18], "compress": 0, "sens": 0, "deep": 0, "requir": 0, "dl": 0, "refer": 0, "introduct": [1, 7], "comparison": 1, "displac": 1, "motion": 1, "flow": 1, "exampl": [1, 10, 11, 12], "alias": 1, "distort": 1, "t2": [1, 5, 11], "simul": [1, 5, 10, 16, 24], "field": [2, 13, 15, 16, 17, 22], "view": 2, "fov": [2, 18], "resolut": [2, 18, 20], "spatial": [2, 9, 18, 22, 23], "fast": [3, 9, 18], "puls": [3, 4, 5, 9, 10, 17, 18, 19, 23], "sequenc": [3, 5, 9, 17, 18], "multipl": 3, "spin": [3, 5, 9, 24], "echo": [3, 5], "rare": 3, "fse": 3, "tse": 3, "simplifi": [3, 17], "diagram": [3, 17], "paramet": [3, 17], "tradeoff": 3, "planar": 3, "epi": 3, "k": [3, 6, 8, 12, 14, 22], "space": [3, 6, 8, 12, 13, 14, 22], "gradient": [3, 5, 15, 16, 17, 22], "spoiler": 3, "crusher": 3, "rf": [3, 4, 9, 10, 15, 16, 17, 18, 19, 23], "spoil": 3, "type": 3, "fun": 4, "adiabat": 4, "pretti": 4, "pictur": 4, "ge": 5, "gre": 5, "off": [5, 14, 19], "reson": [5, 14, 16, 19, 24], "effect": [5, 22], "refocus": 5, "visual": 5, "se": 5, "sort": 6, "data": [6, 12, 14, 17, 20, 22], "transform": [6, 12], "principl": 7, "get": 7, "start": 7, "cours": 7, "lectur": 7, "us": 7, "educ": 7, "resourc": [7, 21], "code": 7, "acknowledg": 7, "cartesian": 8, "frequenc": [8, 24], "phase": 8, "encod": [8, 9, 18, 22], "ft": [8, 9], "trajectori": 8, "kei": [9, 17], "concept": [9, 12], "equat": [9, 10, 14, 20, 24], "background": 9, "materi": 9, "mr": [9, 18], "physic": [9, 18, 24], "system": [9, 15, 16, 18], "experi": [9, 15], "contrast": [9, 11, 18], "In": 9, "vivo": 9, "characterist": [9, 18], "bloch": 10, "THE": 10, "precess": [10, 24], "excit": [10, 16, 17, 19, 24], "constant": 10, "amplitud": 10, "lab": 10, "versu": [10, 19, 20], "rotat": 10, "frame": 10, "common": 10, "flip": [10, 11, 19], "angl": [10, 11, 19], "relax": [10, 14, 24], "what": 11, "determin": 11, "t1": 11, "valu": 11, "typic": 11, "1": 11, "5": 11, "t": [11, 15, 16], "3": 11, "te": 11, "tr": [11, 20], "90": 11, "degre": 11, "proton": 11, "densiti": 11, "weight": [11, 14], "pd": 11, "invers": [11, 12], "recoveri": 11, "agent": 11, "fat": 11, "water": 11, "simpl": 11, "phantom": 11, "challeng": 11, "yourself": 11, "math": 12, "complex": 12, "number": 12, "impuls": 12, "function": 12, "train": 12, "sampl": [12, 17], "other": 12, "convolut": 12, "2": 12, "d": 12, "n": 12, "dualiti": 12, "separ": 12, "ident": 12, "pair": 12, "truncat": 12, "point": 12, "spread": 12, "psf": 12, "analysi": 12, "discret": 12, "notat": 13, "terminolog": 13, "definit": 13, "posit": 13, "net": 13, "magnet": [13, 15, 16, 17, 20, 22, 24], "acronym": 13, "glossari": 13, "The": [14, 15, 17], "signal": [14, 16, 20, 22], "ideal": 14, "ad": 14, "coil": [14, 15, 16, 18], "sensit": [14, 16], "dure": 14, "acquisit": [14, 17, 20], "chemic": 14, "shift": [14, 19], "complet": 14, "compon": [15, 17], "scanner": 15, "main": [15, 16], "b_0": [15, 16], "radiofrequ": [15, 16], "b_1": [15, 16], "vec": [15, 16], "r": [15, 16], "g": [15, 16], "fundament": 15, "procedur": 15, "loop": 16, "current": 16, "transmit": 16, "tx": 16, "receiv": 16, "rx": 16, "recept": 16, "creat": 16, "reciproc": 16, "profil": 16, "element": 16, "local": 17, "g_x": 17, "g_y": 17, "g_z": 17, "window": 17, "daq": 17, "annot": 17, "question": 18, "properti": 19, "time": [19, 20], "bandwidth": 19, "product": 19, "slice": 19, "thick": 19, "specif": 19, "absorpt": 19, "rate": 19, "select": 19, "hard": 19, "shape": 19, "On": 19, "design": [19, 23], "high": 19, "nois": 20, "ratio": 20, "depend": 20, "voxel": 20, "volum": 20, "transvers": 20, "effici": 20, "post": 20, "process": 20, "upsampl": 20, "downsampl": 20, "t_2": 20, "decai": 20, "softwar": 21, "from": 22, "spectral": 23, "nuclear": 24, "polar": 24, "equilibrium": 24, "fraction": 24}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 6, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx": 56}})
\ No newline at end of file