Scalable Double Regularization for 3D Nano-CT Reconstruction

We utilize the entire 3D Nano-CT volume for simultaneous 3D structural reconstruction across slices through total variation regularization within slices and $L_1$ regularization between adjacent slices.

Examples

The followling demonstration is also in the main_simulation.m script.

Global parameter setting

% Global set: Necessary for both simulation and real data
resolution=128; thetaresolution=1; width=0.7;
nol=resolution*180/thetaresolution;
nop=resolution*resolution;dimension=1;
simulation=true; 
[len,loc,len_width,loc_width] = load_matrix_A(thetaresolution,resolution,dimension,width);
globalstruct=struct('resolution',resolution,'thetaresolution',thetaresolution,'len_width',len_width,'loc_width',loc_width);

If simulation is set as true, the code will use simulated data. For real data application, set simulation as false and put observations into one directory and save the path of this directory to the variable pro_direction.

Simulate 3D CT projection data 'pro' using 3D Shepp-logan model

ph=phantom3d(resolution);
AF1=squeeze(ph(:,:,test_slice));

noise_parameter=struct();
noise_parameter.resolution=resolution;
% Add Gaussian noise 
noise_parameter.add_gaussian=1; % 1 to indicate adding gaussian noise. If 1 is chosen, then users should specify noise_paramter.gaussian
noise_parameter.gaussian=0.5; % standard derivation of Gaussian noise 

% Add blank edges 
noise_parameter.add_blankedges=1;% 1 to indicate adding blankedges. If 1 is chosen, then users should specify noise_parameter.blankedges_ratio
noise_parameter.blankedges_ratio=0.15; % Higher ratio means more blank edges. 

Calculate FBP reconstructions

% Reconstruct all slices of the data (from the first to the last). 
% Users can find the reconstructions from the directory saved in FBP_result_direct.
FBP_result_direct=FBP_algorithm(pro_direction,globalstruct);

Calculate SDR reconstructions

% First Set for SDR param.
SDR_param=struct();
SDR_param.TVresidual=-1;% if residual choose less than 0, then stop rule is iteration times
SDR_param.TVmaxIte=4;
SDR_param.TVSHUF=true;
SDR_param.OutmaxIte=3;
%SDR_param.top=floor(size(pro,2)*0.3);
%SDR_param.bottom=floor(size(pro,2)*0.8);
SDR_param.top=38;
SDR_param.bottom=70;

% Reconstruct all slices ranging from specified `top` to `bottom` of the data. 
% Users can find reconstructions from the directory saved in `directnew`. 
directnew = SDR_algorithm(globalstruct,SDR_param,pro_direction);

Result

We compare the reconstructions by FBP and SDR using the 60th slice: