Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

ENH: Add SH order theory #106

Merged
merged 3 commits into from
Mar 28, 2021
Merged

ENH: Add SH order theory #106

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
3 commits
Select commit Hold shift + click to select a range
326b1e6
add a little bit of theory between SD and SH
kaitj Mar 28, 2021
cb08502
STY: Fix grammatical errors, revert cartesian vs trigonometric
kaitj Mar 28, 2021
83c6995
fix extra s
kaitj Mar 28, 2021
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
5 changes: 3 additions & 2 deletions _episodes/constrained_spherical_deconvolution.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -41,7 +41,7 @@ In order to perform the deconvolution over the sphere, the spherical
representation of the diffusion data has to be obtained. This is done using the
so-called Spherical Harmonics (SH) which are a basis that allow to represent
any function on the sphere (much like the Fourier analysis allows to represent
a function in terms of in terms of trigonometric functions).
a function in terms of trigonometric functions).

In this episode we will be using the Constrained Spherical Deconvolution (CSD)
method proposed by Tournier *et al*. in 2007. In essence, CSD imposes a
Expand Down Expand Up @@ -209,7 +209,8 @@ and hence it must be computed on a case basis.
After estimating a response function, the fODF is reconstructed through the
deconvolution operation. In order to obtain the spherical representation of the
diffusion signal, the order of the Spherical Harmonics expansion must be
specified. The series is infinite, but must be truncated to a maximum order in
specified. The order, $l$, corresponds to an angular frequency of the basis function.
While the series is infinite, it must be truncated to a maximum order in
practice to be able to represent the diffusion signal. The maximum order will
determine the number of SH coefficients used. The number of diffusion encoding
gradient directions must be at least as large as the number of coefficients.
Expand Down
8 changes: 4 additions & 4 deletions code/constrained_spherical_deconvolution/constrained_spherical_deconvolution.ipynb
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -21,8 +21,8 @@
"In order to perform the deconvolution over the sphere, the spherical\n",
"representation of the diffusion data has to be obtained. This is done using the\n",
"so-called Spherical Harmonics (SH) which are a basis that allow to represent any\n",
"function on the sphere (much like the Fourier analysis allows to represent a\n",
"function in terms of in terms of trigonometric functions).\n",
"function on the sphere (much like the Fourier analysis allows to represent\n",
"a function in terms of trigonometric functions).\n",
"\n",
"In this episode we will be using the Constrained Spherical Deconvolution (CSD)\n",
"method proposed by Tournier *et al*. in 2007. In essence, CSD imposes a\n",
Expand Down Expand Up @@ -248,7 +248,7 @@
"After estimating a response function, the fODF is reconstructed through the\n",
"deconvolution operation. In order to obtain the spherical representation of the\n",
"diffusion signal, the order of the Spherical Harmonics expansion must be\n",
"specified. The series is infinite, but must be truncated to a maximum order in\n",
"specified. The order, $l$, corresponds to an angular frequency of the basis function. While the series is infinite, it must be truncated to a maximum order in\n",
"practice to be able to represent the diffusion signal. The maximum order will\n",
"determine the number of SH coefficients used. The number of diffusion encoding\n",
"gradient directions must be at least as large as the number of coefficients.\n",
Expand Down Expand Up @@ -541,4 +541,4 @@
},
"nbformat": 4,
"nbformat_minor": 4
}
}