+% Demonstration of tomographic reconstruction from noisy and corrupted by

+% artifacts undersampled projection data using Students't penalty

+% Optimisation problem is solved using FISTA algorithm (see Beck & Teboulle)

+

+% see Readme file for instructions

+%%

+% compile MEX-files ones

+% cd ..

+% cd main_func

+% compile_mex

+% cd ..

+% cd demos

+%%

+

+close all;clc;clear all;

+% adding paths

+addpath('../data/');

+addpath('../main_func/');

+addpath('../supp/');

+

+load phantom_bone512.mat % load the phantom

+load my_red_yellowMAP.mat % load the colormap

+% load sino1.mat; % load noisy sinogram

+

+N = 512; % the size of the tomographic image NxN

+theta = 1:1:180; % acquisition angles (in parallel beam from 0 to Pi)

+theta_rad = theta*(pi/180); % conversion to radians

+P = 2*ceil(N/sqrt(2))+1; % the size of the detector array

+ROI = find(phantom > 0);

+

+% using ASTRA to set the projection geometry

+% potentially parallel geometry can be replaced with a divergent one

+Z_slices = 1;

+det_row_count = Z_slices;

+proj_geom = astra_create_proj_geom('parallel3d', 1, 1, det_row_count, P, theta_rad);

+vol_geom = astra_create_vol_geom(N,N,Z_slices);

+

+zing_rings_add; % generating data, adding zingers and stripes

+%%

+fprintf('%s\n', 'Direct reconstruction using FBP...');

+FBP_1 = iradon(sino_zing_rings', theta, N);

+

+fprintf('%s %.4f\n', 'RMSE for FBP reconstruction:', RMSE(FBP_1(:), phantom(:)));

+

+figure(1);

+subplot_tight(1,2,1, [0.05 0.05]); imshow(FBP_1,[0 0.6]); title('FBP reconstruction of noisy and corrupted by artifacts sinogram'); colorbar;

+subplot_tight(1,2,2, [0.05 0.05]); imshow((phantom - FBP_1).^2,[0 0.1]); title('residual: (ideal phantom - FBP)^2'); colorbar;

+colormap(cmapnew);

+

+%%

+fprintf('%s\n', 'Reconstruction using FISTA-PWLS without regularization...');

+clear params

+% define parameters

+params.proj_geom = proj_geom; % pass geometry to the function

+params.vol_geom = vol_geom;

+params.sino = sino_zing_rings; % sinogram

+params.iterFISTA = 45; %max number of outer iterations

+params.X_ideal = phantom; % ideal phantom

+params.ROI = ROI; % phantom region-of-interest

+params.show = 1; % visualize reconstruction on each iteration

+params.slice = 1; params.maxvalplot = 0.6;

+params.weights = Dweights; % statistical weighting

+tic; [X_FISTA, output] = FISTA_REC(params); toc;

+

+fprintf('%s %.4f\n', 'Min RMSE for FISTA-PWLS reconstruction is:', min(error_FISTA(:)));

+error_FISTA = output.Resid_error; obj_FISTA = output.objective;

+

+figure(2); clf

+%set(gcf, 'Position', get(0,'Screensize'));

+subplot_tight(1,2,1, [0.05 0.05]); imshow(X_FISTA,[0 0.6]); title('FISTA-PWLS reconstruction'); colorbar;

+subplot_tight(1,2,2, [0.05 0.05]); imshow((phantom - X_FISTA).^2,[0 0.1]); title('residual'); colorbar;

+colormap(cmapnew);

+figure(3); clf

+subplot_tight(1,2,1, [0.05 0.05]); plot(error_FISTA); title('RMSE plot'); colorbar;

+subplot_tight(1,2,2, [0.05 0.05]); plot(obj_FISTA); title('Objective plot'); colorbar;

+colormap(cmapnew);

+%%

+fprintf('%s\n', 'Reconstruction using FISTA-PWLS-TV...');

+clear params

+% define parameters

+params.proj_geom = proj_geom; % pass geometry to the function

+params.vol_geom = vol_geom;

+params.sino = sino_zing_rings;

+params.iterFISTA = 45; % max number of outer iterations

+params.Regul_LambdaTV = 0.0015; % regularization parameter for TV problem

+params.X_ideal = phantom; % ideal phantom

+params.ROI = ROI; % phantom region-of-interest

+params.weights = Dweights; % statistical weighting

+params.show = 1; % visualize reconstruction on each iteration

+params.slice = 1; params.maxvalplot = 0.6;

+tic; [X_FISTA_TV, output] = FISTA_REC(params); toc;

+

+fprintf('%s %.4f\n', 'Min RMSE for FISTA-PWLS-TV reconstruction is:', min(error_FISTA_TV(:)));

+error_FISTA_TV = output.Resid_error; obj_FISTA_TV = output.objective;

+

+figure(4); clf

+subplot_tight(1,2,1, [0.05 0.05]); imshow(X_FISTA_TV,[0 0.6]); title('FISTA-PWLS-TV reconstruction'); colorbar;

+subplot_tight(1,2,2, [0.05 0.05]); imshow((phantom - X_FISTA_TV).^2,[0 0.1]); title('residual'); colorbar;

+colormap(cmapnew);

+figure(5); clf

+subplot_tight(1,2,1, [0.05 0.05]); plot(error_FISTA_TV); title('RMSE plot'); colorbar;

+subplot_tight(1,2,2, [0.05 0.05]); plot(obj_FISTA_TV); title('Objective plot'); colorbar;

+colormap(cmapnew);

+%%

+fprintf('%s\n', 'Reconstruction using FISTA-GH-TV...');

+clear params

+% define parameters

+params.proj_geom = proj_geom; % pass geometry to the function

+params.vol_geom = vol_geom;

+params.sino = sino_zing_rings;

+params.iterFISTA = 50; % max number of outer iterations

+params.Regul_LambdaTV = 0.0015; % regularization parameter for TV problem

+params.X_ideal = phantom; % ideal phantom

+params.ROI = ROI; % phantom region-of-interest

+params.weights = Dweights; % statistical weighting

+params.Ring_LambdaR_L1 = 0.002; % parameter to sparsify the "rings vector"

+params.Ring_Alpha = 20; % to accelerate ring-removal procedure

+params.show = 0; % visualize reconstruction on each iteration

+params.slice = 1; params.maxvalplot = 0.6;

+tic; [X_FISTA_GH_TV, output] = FISTA_REC(params); toc;

+

+fprintf('%s %.4f\n', 'Min RMSE for FISTA-GH-TV reconstruction is:', min(error_FISTA_GH_TV(:)));

+error_FISTA_GH_TV = output.Resid_error; obj_FISTA_GH_TV = output.objective;

+

+figure(6); clf

+subplot_tight(1,2,1, [0.05 0.05]); imshow(X_FISTA_GH_TV,[0 0.6]); title('FISTA-GH-TV reconstruction'); colorbar;

+subplot_tight(1,2,2, [0.05 0.05]);imshow((phantom - X_FISTA_GH_TV).^2,[0 0.1]); title('residual'); colorbar;

+colormap(cmapnew);

+

+figure(7); clf

+subplot_tight(1,2,1, [0.05 0.05]); plot(error_FISTA_GH_TV); title('RMSE plot'); colorbar;

+subplot_tight(1,2,2, [0.05 0.05]); plot(obj_FISTA_GH_TV); title('Objective plot'); colorbar;

+colormap(cmapnew);

+%%

+fprintf('%s\n', 'Reconstruction using FISTA-Student-TV...');

+clear params

+% define parameters

+params.proj_geom = proj_geom; % pass geometry to the function

+params.vol_geom = vol_geom;

+params.sino = sino_zing_rings;

+params.iterFISTA = 55; % max number of outer iterations

+params.L_const = 0.1; % Lipshitz constant (can be chosen manually to accelerate convergence)

+params.Regul_LambdaTV = 0.00152; % regularization parameter for TV problem

+params.X_ideal = phantom; % ideal phantom

+params.ROI = ROI; % phantom region-of-interest

+params.weights = Dweights; % statistical weighting

+params.fidelity = 'student'; % selecting students t fidelity

+params.show = 1; % visualize reconstruction on each iteration

+params.slice = 1; params.maxvalplot = 0.6;

+params.initilize = 1; % warm start with SIRT

+tic; [X_FISTA_student_TV, output] = FISTA_REC(params); toc;

+

+fprintf('%s %.4f\n', 'Min RMSE for FISTA-Student-TV reconstruction is:', min(error_FISTA_student_TV(:)));

+error_FISTA_student_TV = output.Resid_error; obj_FISTA_student_TV = output.objective;

+

+figure(8);

+set(gcf, 'Position', get(0,'Screensize'));

+subplot_tight(1,2,1, [0.05 0.05]); imshow(X_FISTA_student_TV,[0 0.6]); title('FISTA-Student-TV reconstruction'); colorbar;

+subplot_tight(1,2,2, [0.05 0.05]); imshow((phantom - X_FISTA_student_TV).^2,[0 0.1]); title('residual'); colorbar;

+colormap(cmapnew);

+

+figure(9);

+subplot_tight(1,2,1, [0.05 0.05]); plot(error_FISTA_student_TV); title('RMSE plot'); colorbar;

+subplot_tight(1,2,2, [0.05 0.05]); plot(obj_FISTA_student_TV); title('Objective plot'); colorbar;

+colormap(cmapnew);

+%%

+% print all RMSE's

+fprintf('%s\n', '--------------------------------------------');

+fprintf('%s %.4f\n', 'RMSE for FBP reconstruction:', RMSE(FBP_1(:), phantom(:)));

+fprintf('%s %.4f\n', 'Min RMSE for FISTA-PWLS reconstruction:', min(error_FISTA(:)));

+fprintf('%s %.4f\n', 'Min RMSE for FISTA-PWLS-TV reconstruction:', min(error_FISTA_TV(:)));

+fprintf('%s %.4f\n', 'Min RMSE for FISTA-GH-TV reconstruction:', min(error_FISTA_GH_TV(:)));

+fprintf('%s %.4f\n', 'Min RMSE for FISTA-Student-TV reconstruction:', min(error_FISTA_student_TV(:)));

+% \ No newline at end of file