% 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('../main_func/regularizers_CPU/'); 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(1,2,1, [0.05 0.05]); imshow(X_FISTA,[0 0.6]); title('FISTA-PWLS reconstruction'); colorbar; subplot(1,2,2, [0.05 0.05]); imshow((phantom - X_FISTA).^2,[0 0.1]); title('residual'); colorbar; colormap(cmapnew); figure(3); clf subplot(1,2,1, [0.05 0.05]); plot(error_FISTA); title('RMSE plot'); colorbar; subplot(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(1,2,1, [0.05 0.05]); imshow(X_FISTA_TV,[0 0.6]); title('FISTA-PWLS-TV reconstruction'); colorbar; subplot(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(1,2,1, [0.05 0.05]); plot(error_FISTA_TV); title('RMSE plot'); colorbar; subplot(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(1,2,1, [0.05 0.05]); imshow(X_FISTA_GH_TV,[0 0.6]); title('FISTA-GH-TV reconstruction'); colorbar; subplot(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(1,2,1, [0.05 0.05]); plot(error_FISTA_GH_TV); title('RMSE plot'); colorbar; subplot(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(1,2,1, [0.05 0.05]); imshow(X_FISTA_student_TV,[0 0.6]); title('FISTA-Student-TV reconstruction'); colorbar; subplot(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(1,2,1, [0.05 0.05]); plot(error_FISTA_student_TV); title('RMSE plot'); colorbar; subplot(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(:))); %