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authorPasca <edoardo.pasca@stfc.ac.uk>2017-03-29 16:46:28 +0100
committerPasca <edoardo.pasca@stfc.ac.uk>2017-03-29 16:46:28 +0100
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Initial revision
-rw-r--r--Readme.md82
-rw-r--r--data/phantom_bone512.matbin0 -> 408035 bytes
-rw-r--r--data/sino3D_dendrites.matbin0 -> 27797233 bytes
-rw-r--r--data/sino_basalt.matbin0 -> 1109887 bytes
-rw-r--r--demo/Demo1.m160
-rw-r--r--demo/Demo2.m156
-rw-r--r--demo/DemoRD1.m99
-rw-r--r--demo/DemoRD2.m130
-rw-r--r--license.txt27
-rw-r--r--main_func/FISTA_REC.m338
-rw-r--r--main_func/FISTA_TV.c331
-rw-r--r--main_func/LLT_model.c431
-rw-r--r--main_func/SplitBregman_TV.c346
-rw-r--r--main_func/compile_mex.m4
-rw-r--r--main_func/studentst.m47
-rw-r--r--readme.docbin0 -> 21504 bytes
-rw-r--r--readme.pdfbin0 -> 61855 bytes
-rw-r--r--supp/RMSE.m7
-rw-r--r--supp/add_wedges.m30
-rw-r--r--supp/filtersinc.m28
-rw-r--r--supp/my_red_yellowMAP.matbin0 -> 1761 bytes
-rw-r--r--supp/ssim_index.m181
-rw-r--r--supp/subplot_tight.m1
-rw-r--r--supp/zing_rings_add.m84
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diff --git a/Readme.md b/Readme.md
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+# FISTA Reconstruction (Daniil Kazanteev)
+
+# General Description
+
+Software for reconstructing 2D/3D x-ray and neutron tomography datasets. The data can be undersampled, of poor contrast, noisy, and contain various artifacts. This is Matlab and C-omp implementation of iterative model-based algorithms with unconventional data fidelities and with various regularization terms (TV and higher-order LLT). The main optimization problem is solved using FISTA framework [1]. The presented algorithms are FBP, FISTA (Least-Squares), FISTA-LS-TV(LS-Total Variation), FISTA-GH(Group-Huber)-TV, and FISTA-Student-TV. More information about the algorithms can be found in papers [2,3]. Please cite [2] if the algorithms or data used in your research.
+
+## Requirements/Dependencies:
+
+ * MATLAB (www.mathworks.com/products/matlab/)
+ * ASTRA toolbox (https://github.com/astra-toolbox/astra-toolbox)
+ * C/C++ compiler (run compile_mex in Matlab first to compile C-functions)
+
+## Package Contents:
+
+### Demos:
+ * Demo1: Synthetic phantom reconstruction with noise, stripes and zingers
+ * Demo2: Synthetic phantom reconstruction with noise, stripes, zingers, and the missing wedges
+ * DemoRD1: Real data reconstruction from sino_basalt.mat (see Data)
+ * DemoRD2: Real data reconstruction from sino3D_dendrites.mat (see Data)
+
+### Data:
+ * phantom_bone512.mat - a synthetic 2D phantom obtained from high-resolution x-ray scan
+ * sino_basalt.mat – 2D neutron (PSI) tomography sinogram (slice across a pack of basalt beads)
+ * sino3D_dendrites.mat – 3D (20 slices) x-ray synchrotron dataset (DLS) of growing dendrites
+
+### Main modules:
+
+ * FISTA_REC.m – Matlab function to perform FISTA-based reconstruction
+ * FISTA_TV.c – C-omp function to solve for the weighted TV term using FISTA
+ * SplitBregman_TV.c – C-omp function to solve for the weighted TV term using Split-Bregman
+ * LLT_model.c – C-omp function to solve for the weighted LLT [3] term using explicit scheme
+ * studentst.m – Matlab function to calculate Students t penalty with 'auto-tuning'
+
+### Supplementary:
+
+ * zing_rings_add.m Matlab script to generate proj. data, add noise, zingers and stripes
+ * add_wedges.m script to add the missing wedge to existing sinogram
+ * my_red_yellowMAP.mat – nice colormap for the phantom
+ * RMSE.m – Matlab function to calculate Root Mean Square Error
+ * subplot_tight – visualizing better subplots
+ * ssim_index – ssim calculation
+
+### Practical advices:
+ * Full 3D reconstruction provides much better results than 2D. In the case of ring artifacts, 3D is almost necessary
+ * Depending on data it is better to use TV-LLT combination in order to achieve piecewise-smooth solution. The DemoRD2 shows one possible example when smoother surfaces required.
+ * L (Lipshitz constant) if tweaked can lead to faster convergence than automatic values
+ * Convergence is normally much faster when using Fourier filtering before backprojection
+ * Students’t penalty is generally quite stable in practice, however some tweaking of L might require for the real data
+ * You can choose between SplitBregman-TV and FISTA-TV modules. The former is slower but requires less memory (for 3D volume U it can take up to 6 x U), the latter is faster but can take more memory (for 3D volume U it can take up to 11 x U). Also the SplitBregman is quite good in improving contrast.
+
+ ### Compiling:
+
+ It is very important to check that OMP support is activated for the optimal use of all CPU cores.
+#### Windows
+ In Windows enable OMP support, e.g.:
+edit C:\Users\Username\AppData\Roaming\MathWorks\MATLAB\R2012b\mexopts.bat
+In the file, edit 'OPTIMFLAGS' line as shown below (add /openmp entry at the end):
+OPTIMFLAGS = /O2 /Oy- /DNDEBUG /openmp
+define and set the number of CPU cores
+PROC = feature('numCores');
+PROCS = num2str(PROC);
+setenv('OMP_NUM_THREADS', PROCS); % you can check how many CPU's by: getenv
+OMP_NUM_THREADS
+
+#### Linux
+In Linux in terminal: export OMP_NUM_THREADS = (the numer of CPU cores)
+then run Matlab as normal
+to compile with OMP support from Matlab in Windows run:
+mex *.cpp CFLAGS="\$CFLAGS -fopenmp -Wall" LDFLAGS="\$LDFLAGS -fopenmp"
+to compile with OMP support from Matlab in Linux ->rename *cpp to *c and compile:
+mex *.c CFLAGS="\$CFLAGS -fopenmp -Wall" LDFLAGS="\$LDFLAGS -fopenmp"
+
+
+### References:
+[1] Beck, A. and Teboulle, M., 2009. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM journal on imaging sciences,2(1), pp.183-202.
+[2] Kazantsev, D., Bleichrodt, F., van Leeuwen, T., Kaestner, A., Withers, P.J., Batenburg, K.J., 2017. A novel tomographic reconstruction method based on the robust Student's t function for suppressing data outliers, IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING (to appear)
+[3] Lysaker, M., Lundervold, A. and Tai, X.C., 2003. Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Transactions on image processing, 12(12), pp.1579-1590.
+[4] Paleo, P. and Mirone, A., 2015. Ring artifacts correction in compressed sensing tomographic reconstruction. Journal of synchrotron radiation, 22(5), pp.1268-1278.
+[5] Sidky, E.Y., Jakob, H.J. and Pan, X., 2012. Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm. Physics in medicine and biology, 57(10), p.3065.
+
+D. Kazantsev / Harwell Campus / 16.03.17
+any questions/comments please e-mail to daniil.kazantsev@manchester.ac.uk
diff --git a/data/phantom_bone512.mat b/data/phantom_bone512.mat
new file mode 100644
index 0000000..ae3c7d8
--- /dev/null
+++ b/data/phantom_bone512.mat
Binary files differ
diff --git a/data/sino3D_dendrites.mat b/data/sino3D_dendrites.mat
new file mode 100644
index 0000000..dc1400d
--- /dev/null
+++ b/data/sino3D_dendrites.mat
Binary files differ
diff --git a/data/sino_basalt.mat b/data/sino_basalt.mat
new file mode 100644
index 0000000..164d144
--- /dev/null
+++ b/data/sino_basalt.mat
Binary files differ
diff --git a/demo/Demo1.m b/demo/Demo1.m
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index 0000000..08d46e1
--- /dev/null
+++ b/demo/Demo1.m
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+% 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
+clear all
+close 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);
+
+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-LS without regularization...');
+clear params
+% define parameters
+params.sino = sino_zing_rings;
+params.N = N; % image size
+params.angles = theta_rad; % angles in radians
+params.iterFISTA = 180; %max number of outer iterations
+params.X_ideal = phantom; % ideal phantom
+params.ROI = ROI; % phantom region-of-interest
+params.show = 0; % visualize reconstruction on each iteration
+params.slice = 1; params.maxvalplot = 0.6;
+params.weights = Dweights; % statistical weighting
+tic; [X_FISTA, error_FISTA, obj_FISTA, sinoFISTA] = FISTA_REC(params); toc;
+
+fprintf('%s %.4f\n', 'Min RMSE for FISTA-LS reconstruction is:', min(error_FISTA(:)));
+
+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-LS 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-LS-TV...');
+clear params
+% define parameters
+params.sino = sino_zing_rings;
+params.N = N; % image size
+params.angles = theta_rad; % angles in radians
+params.iterFISTA = 200; % max number of outer iterations
+params.lambdaTV = 5.39e-05; % regularization parameter for TV problem
+params.tol = 1.0e-04; % tolerance to terminate TV iterations
+params.iterTV = 20; % the max number of TV iterations
+params.X_ideal = phantom; % ideal phantom
+params.ROI = ROI; % phantom region-of-interest
+params.weights = Dweights; % statistical weighting
+params.show = 0; % visualize reconstruction on each iteration
+params.slice = 1; params.maxvalplot = 0.6;
+tic; [X_FISTA_TV, error_FISTA_TV, obj_FISTA_TV, sinoFISTA_TV] = FISTA_REC(params); toc;
+
+fprintf('%s %.4f\n', 'Min RMSE for FISTA-LS-TV reconstruction is:', min(error_FISTA_TV(:)));
+
+figure(4); clf
+subplot_tight(1,2,1, [0.05 0.05]); imshow(X_FISTA_TV,[0 0.6]); title('FISTA-LS-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.sino = sino_zing_rings;
+params.N = N; % image size
+params.angles = theta_rad; % angles in radians
+params.iterFISTA = 60; % max number of outer iterations
+params.lambdaTV = 0.002526; % regularization parameter for TV problem
+params.tol = 1.0e-04; % tolerance to terminate TV iterations
+params.iterTV = 20; % the max number of TV iterations
+params.X_ideal = phantom; % ideal phantom
+params.ROI = ROI; % phantom region-of-interest
+params.weights = Dweights; % statistical weighting
+params.lambdaR_L1 = 0.002; % parameter to sparsify the "rings vector"
+params.show = 0; % visualize reconstruction on each iteration
+params.slice = 1; params.maxvalplot = 0.6;
+tic; [X_FISTA_GH_TV, error_FISTA_GH_TV, obj_FISTA_GH_TV, sinoFISTA_GH_TV] = FISTA_REC(params); toc;
+
+fprintf('%s %.4f\n', 'Min RMSE for FISTA-GH-TV reconstruction is:', min(error_FISTA_GH_TV(:)));
+
+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.sino = sino_zing_rings;
+params.N = N; % image size
+params.angles = theta_rad; % angles in radians
+params.iterFISTA = 67; % max number of outer iterations
+%params.L_const = 80000; % Lipshitz constant (can be chosen manually to accelerate convergence)
+params.lambdaTV = 0.00152; % regularization parameter for TV problem
+params.tol = 1.0e-04; % tolerance to terminate TV iterations
+params.iterTV = 20; % the max number of TV iterations
+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 = 0; % visualize reconstruction on each iteration
+params.slice = 1; params.maxvalplot = 0.6;
+tic; [X_FISTA_student_TV, error_FISTA_student_TV, obj_FISTA_student_TV, sinoFISTA_student_TV] = FISTA_REC(params); toc;
+
+fprintf('%s %.4f\n', 'Min RMSE for FISTA-Student-TV reconstruction is:', min(error_FISTA_student_TV(:)));
+
+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_2(:), phantom(:)));
+fprintf('%s %.4f\n', 'Min RMSE for FISTA-LS reconstruction:', min(error_FISTA(:)));
+fprintf('%s %.4f\n', 'Min RMSE for FISTA-LS-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
diff --git a/demo/Demo2.m b/demo/Demo2.m
new file mode 100644
index 0000000..3c1592c
--- /dev/null
+++ b/demo/Demo2.m
@@ -0,0 +1,156 @@
+% Demonstration of tomographic reconstruction from noisy and corrupted by
+% artifacts undersampled projection data using Students t penalty
+% This is the missing wedge demo, run it after DemoFISTA_StudT
+
+% see ReadMe file for instructions
+% clear all
+% close all
+
+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 > 0.0);
+
+add_wedges % apply the missing wedge mask
+
+%%
+fprintf('%s\n', 'Direct reconstruction using FBP...');
+FBP_1 = iradon(MW_sino_artifacts', theta, N);
+
+fprintf('%s %.4f\n', 'RMSE for FBP reconstruction:', RMSE(FBP_1(:), phantom(:)));
+
+figure(1);
+% set(gcf, 'Position', get(0,'Screensize'));
+subplot_tight(1,2,1, [0.05 0.05]); imshow(FBP_1,[-2 0.8]); 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-LS without regularization...');
+clear params
+% define parameters
+params.sino = MW_sino_artifacts;
+params.N = N; % image size
+params.angles = theta_rad; % angles in radians
+params.iterFISTA = 132; %max number of outer iterations
+params.X_ideal = phantom; % ideal phantom
+params.ROI = ROI; % phantom region-of-interest
+params.show = 0; % visualize reconstruction on each iteration
+params.slice = 1; params.maxvalplot = 0.6;
+params.weights = Dweights; % statistical weighting
+tic; [X_FISTA, error_FISTA, obj_FISTA, sinoFISTA] = FISTA_REC(params); toc;
+
+fprintf('%s %.4f\n', 'Min RMSE for FISTA-LS reconstruction:', min(error_FISTA(:)));
+
+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-LS 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-LS-TV...');
+clear params
+% define parameters
+params.sino = MW_sino_artifacts;
+params.N = N; % image size
+params.angles = theta_rad; % angles in radians
+params.iterFISTA = 200; % max number of outer iterations
+params.lambdaTV = 5.39e-05; % regularization parameter for TV problem
+params.tol = 1.0e-04; % tolerance to terminate TV iterations
+params.iterTV = 20; % the max number of TV iterations
+params.X_ideal = phantom; % ideal phantom
+params.ROI = ROI; % phantom region-of-interest
+params.weights = Dweights; % statistical weighting
+params.show = 0; % visualize reconstruction on each iteration
+params.slice = 1; params.maxvalplot = 0.6;
+tic; [X_FISTA_TV, error_FISTA_TV, obj_FISTA_TV, sinoFISTA_TV] = FISTA_REC(params); toc;
+
+fprintf('%s %.4f\n', 'Min RMSE for FISTA-LS-TV reconstruction:', min(error_FISTA_TV(:)));
+
+figure(4); clf
+subplot_tight(1,2,1, [0.05 0.05]); imshow(X_FISTA_TV,[0 0.6]); title('FISTA-LS-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.sino = MW_sino_artifacts;
+params.N = N; % image size
+params.angles = theta_rad; % angles in radians
+params.iterFISTA = 250; % max number of outer iterations
+params.lambdaTV = 0.0019; % regularization parameter for TV problem
+params.tol = 1.0e-04; % tolerance to terminate TV iterations
+params.iterTV = 20; % the max number of TV iterations
+params.X_ideal = phantom; % ideal phantom
+params.ROI = ROI; % phantom region-of-interest
+params.weights = Dweights; % statistical weighting
+params.lambdaR_L1 = 0.002; % parameter to sparsify the "rings vector"
+params.show = 0; % visualize reconstruction on each iteration
+params.slice = 1; params.maxvalplot = 0.6;
+tic; [X_FISTA_GH_TV, error_FISTA_GH_TV, obj_FISTA_GH_TV, sinoFISTA_GH_TV] = FISTA_REC(params); toc;
+
+fprintf('%s %.4f\n', 'Min RMSE for FISTA-GH-TV reconstruction:', min(error_FISTA_GH_TV(:)));
+
+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.sino = MW_sino_artifacts;
+params.N = N; % image size
+params.angles = theta_rad; % angles in radians
+params.iterFISTA = 80; % max number of outer iterations
+% params.L_const = 80000; % Lipshitz constant (can be chosen manually to accelerate convergence)
+params.lambdaTV = 0.0016; % regularization parameter for TV problem
+params.tol = 1.0e-04; % tolerance to terminate TV iterations
+params.iterTV = 20; % the max number of TV iterations
+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 = 0; % visualize reconstruction on each iteration
+params.slice = 1; params.maxvalplot = 0.6;
+tic; [X_FISTA_student_TV, error_FISTA_student_TV, obj_FISTA_student_TV, sinoFISTA_student_TV] = FISTA_REC(params); toc;
+
+fprintf('%s %.4f\n', 'Min RMSE for FISTA-Student-TV reconstruction:', min(error_FISTA_student_TV(:)));
+
+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_2(:), phantom(:)));
+fprintf('%s %.4f\n', 'Min RMSE for FISTA-LS reconstruction:', min(error_FISTA(:)));
+fprintf('%s %.4f\n', 'Min RMSE for FISTA-LS-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
diff --git a/demo/DemoRD1.m b/demo/DemoRD1.m
new file mode 100644
index 0000000..9a43cb5
--- /dev/null
+++ b/demo/DemoRD1.m
@@ -0,0 +1,99 @@
+% Demonstration of tomographic reconstruction from neutron tomography
+% dataset (basalt sample) using Student t data fidelity
+clear all
+close all
+
+% adding paths
+addpath('data/');
+addpath('main_func/');
+addpath('supp/');
+
+load('sino_basalt.mat') % load real neutron data
+
+size_det = size(sino_basalt, 1); % detector size
+angSize = size(sino_basalt,2); % angles dim
+recon_size = 650; % reconstruction size
+
+FBP = iradon(sino_basalt, rad2deg(angles),recon_size);
+figure; imshow(FBP , [0, 0.45]); title ('FBP reconstruction');
+
+%%
+fprintf('%s\n', 'Reconstruction using FISTA-LS without regularization...');
+clear params
+params.sino = sino_basalt';
+params.N = recon_size;
+params.angles = angles;
+params.iterFISTA = 50;
+params.show = 0;
+params.maxvalplot = 0.6; params.slice = 1;
+
+tic; [X_fista] = FISTA_REC(params); toc;
+figure; imshow(X_fista , [0, 0.45]); title ('FISTA-LS reconstruction');
+%%
+fprintf('%s\n', 'Reconstruction using FISTA-LS-TV...');
+clear params
+params.sino = sino_basalt';
+params.N = recon_size;
+params.angles = angles;
+params.iterFISTA = 150;
+params.lambdaTV = 0.0003; % TV regularization parameter
+params.tol = 1.0e-04;
+params.iterTV = 20;
+params.show = 1;
+params.maxvalplot = 0.6; params.slice = 1;
+
+tic; [X_fista_TV] = FISTA_REC(params); toc;
+figure; imshow(X_fista_TV , [0, 0.45]); title ('FISTA-LS-TV reconstruction');
+%%
+%%
+fprintf('%s\n', 'Reconstruction using FISTA-GH-TV...');
+clear params
+params.sino = sino_basalt';
+params.N = recon_size;
+params.angles = angles;
+params.iterFISTA = 350;
+params.lambdaTV = 0.0003; % TV regularization parameter
+params.tol = 1.0e-04;
+params.iterTV = 20;
+params.lambdaR_L1 = 0.001; % Soft-Thresh L1 ring variable parameter
+params.show = 1;
+params.maxvalplot = 0.6; params.slice = 1;
+
+tic; [X_fista_GH_TV] = FISTA_REC(params); toc;
+figure; imshow(X_fista_GH_TV , [0, 0.45]); title ('FISTA-GH-TV reconstruction');
+%%
+%%
+fprintf('%s\n', 'Reconstruction using FISTA-Student-TV...');
+clear params
+params.sino = sino_basalt';
+params.N = recon_size;
+params.angles = angles;
+params.iterFISTA = 350;
+params.L_const = 7000; % Lipshitz constant
+params.lambdaTV = 0.0003; % TV regularization parameter
+params.tol = 1.0e-04;
+params.iterTV = 20;
+params.fidelity = 'student'; % choosing Student t penalty
+params.show = 1;
+params.maxvalplot = 0.6; params.slice = 1;
+
+tic; [X_fistaStudentTV] = FISTA_REC(params); toc;
+figure; imshow(X_fistaStudentTV , [0, 0.45]); title ('FISTA-Student-TV reconstruction');
+%%
+
+fprintf('%s\n', 'Segmentation using OTSU method ...');
+level = graythresh(X_fista);
+Segm_FISTA = im2bw(X_fista,level);
+figure; imshow(Segm_FISTA, []); title ('Segmented FISTA-LS reconstruction');
+
+level = graythresh(X_fista_TV);
+Segm_FISTA_TV = im2bw(X_fista_TV,level);
+figure; imshow(Segm_FISTA_TV, []); title ('Segmented FISTA-LS-TV reconstruction');
+
+level = graythresh(X_fista_GH_TV);
+BW_FISTA_GH_TV = im2bw(X_fista_GH_TV,level);
+figure; imshow(BW_FISTA_GH_TV, []); title ('Segmented FISTA-GH-TV reconstruction');
+
+level = graythresh(X_fistaStudentTV);
+BW_FISTA_Student_TV = im2bw(X_fistaStudentTV,level);
+figure; imshow(BW_FISTA_Student_TV, []); title ('Segmented FISTA-Student-LS reconstruction'); \ No newline at end of file
diff --git a/demo/DemoRD2.m b/demo/DemoRD2.m
new file mode 100644
index 0000000..a8ac2ca
--- /dev/null
+++ b/demo/DemoRD2.m
@@ -0,0 +1,130 @@
+% Demonstration of tomographic 3D reconstruction from X-ray synchrotron
+% dataset (dendrites) using various data fidelities
+% clear all
+% close all
+%
+% % adding paths
+ addpath('data/');
+ addpath('main_func/');
+ addpath('supp/');
+
+load('sino3D_dendrites.mat') % load 3D normalized sinogram
+angles_rad = angles*(pi/180); % conversion to radians
+
+angSize = size(Sino3D,1); % angles dim
+size_det = size(Sino3D, 2); % detector size
+recon_size = 850; % reconstruction size
+
+FBP = iradon(Sino3D(:,:,10)', angles,recon_size);
+figure; imshow(FBP , [0, 3]); title ('FBP reconstruction');
+
+%%
+fprintf('%s\n', 'Reconstruction using FISTA-LS without regularization...');
+clear params
+params.sino = Sino3D;
+params.N = recon_size;
+params.angles = angles_rad;
+params.iterFISTA = 80;
+params.precondition = 1; % switch on preconditioning
+params.show = 0;
+params.maxvalplot = 2.5; params.slice = 10;
+
+tic; [X_fista] = FISTA_REC(params); toc;
+figure; imshow(X_fista(:,:,10) , [0, 2.5]); title ('FISTA-LS reconstruction');
+%%
+fprintf('%s\n', 'Reconstruction using FISTA-LS-TV...');
+clear params
+params.sino = Sino3D;
+params.N = recon_size;
+params.angles = angles_rad;
+params.iterFISTA = 100;
+params.lambdaTV = 0.001; % TV regularization parameter for FISTA-TV
+params.tol = 1.0e-04;
+params.iterTV = 20;
+params.precondition = 1; % switch on preconditioning
+params.show = 0;
+params.maxvalplot = 2.5; params.slice = 10;
+
+tic; [X_fista_TV] = FISTA_REC(params); toc;
+figure; imshow(X_fista_TV(:,:,10) , [0, 2.5]); title ('FISTA-LS-TV reconstruction');
+%%
+%%
+fprintf('%s\n', 'Reconstruction using FISTA-GH-TV...');
+clear params
+params.sino = Sino3D;
+params.N = recon_size;
+params.angles = angles_rad;
+params.iterFISTA = 100;
+params.lambdaTV = 0.001; % TV regularization parameter for FISTA-TV
+params.tol = 1.0e-04;
+params.iterTV = 20;
+params.lambdaR_L1 = 0.001; % Soft-Thresh L1 ring variable parameter
+params.alpha_ring = 20; % to boost ring removal procedure
+params.precondition = 1; % switch on preconditioning
+params.show = 0;
+params.maxvalplot = 2.5; params.slice = 10;
+
+tic; [X_fista_GH_TV] = FISTA_REC(params); toc;
+figure; imshow(X_fista_GH_TV(:,:,10) , [0, 2.5]); title ('FISTA-GH-TV reconstruction');
+%%
+%%
+fprintf('%s\n', 'Reconstruction using FISTA-GH-TV-LLT...');
+clear params
+params.sino = Sino3D;
+params.N = recon_size;
+params.angles = angles_rad;
+params.iterFISTA = 100;
+params.lambdaTV = 0.001; % TV regularization parameter for FISTA-TV
+params.tol = 1.0e-04;
+params.iterTV = 20;
+params.lambdaHO = 35; % regularization parameter for LLT problem
+params.tauHO = 0.00011; % time-step parameter for explicit scheme
+params.iterHO = 70; % the max number of TV iterations
+params.lambdaR_L1 = 0.001; % Soft-Thresh L1 ring variable parameter
+params.alpha_ring = 20; % to boost ring removal procedure
+params.precondition = 1; % switch on preconditioning
+params.show = 0;
+params.maxvalplot = 2.5; params.slice = 10;
+
+tic; [X_fista_GH_TVLLT] = FISTA_REC(params); toc;
+figure; imshow(X_fista_GH_TVLLT(:,:,10) , [0, 2.5]); title ('FISTA-GH-TV-LLT reconstruction');
+%%
+%%
+% fprintf('%s\n', 'Reconstruction using FISTA-Student-TV...');
+% %%%%<<<< Not stable with this dataset! Requires more work >>>> %%%%%
+% clear params
+% params.sino = Sino3D(:,:,15);
+% params.N = 950;
+% params.angles = angles_rad;
+% params.iterFISTA = 150;
+% params.L_const = 30; % Lipshitz constant
+% params.lambdaTV = 0.009; % TV regularization parameter for FISTA-TV
+% params.tol = 1.0e-04;
+% params.iterTV = 20;
+% params.fidelity = 'student'; % choosing Student t penalty
+% % params.precondition = 1; % switch on preconditioning
+% params.show = 1;
+% params.maxvalplot = 2.5; params.slice = 1;
+%
+% tic; [X_fistaStudentTV] = FISTA_REC(params); toc;
+% figure; imshow(X_fistaStudentTV , [0, 2.5]); title ('FISTA-Student-TV reconstruction');
+%%
+slice = 10; % if 3D reconstruction
+
+fprintf('%s\n', 'Segmentation using OTSU method ...');
+level = graythresh(X_fista(:,:,slice));
+Segm_FISTA = im2bw(X_fista(:,:,slice),level);
+figure; imshow(Segm_FISTA, []); title ('Segmented FISTA-LS reconstruction');
+
+level = graythresh(X_fista_TV(:,:,slice));
+Segm_FISTA_TV = im2bw(X_fista_TV(:,:,slice),level);
+figure; imshow(Segm_FISTA_TV, []); title ('Segmented FISTA-LS-TV reconstruction');
+
+level = graythresh(X_fista_GH_TV(:,:,slice));
+BW_FISTA_GH_TV = im2bw(X_fista_GH_TV(:,:,slice),level);
+figure; imshow(BW_FISTA_GH_TV, []); title ('Segmented FISTA-GH-TV reconstruction');
+
+level = graythresh(X_fista_GH_TVLLT(:,:,slice));
+BW_FISTA_GH_TVLLT = im2bw(X_fista_GH_TVLLT(:,:,slice),level);
+figure; imshow(BW_FISTA_GH_TVLLT, []); title ('Segmented FISTA-GH-TV-LLT reconstruction');
+%% \ No newline at end of file
diff --git a/license.txt b/license.txt
new file mode 100644
index 0000000..827b7f3
--- /dev/null
+++ b/license.txt
@@ -0,0 +1,27 @@
+Copyright (c) 2017, Daniil Kazantsev, The University of Manchester.
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+ * Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in
+ the documentation and/or other materials provided with the distribution
+ * Neither the name of the nor the names
+ of its contributors may be used to endorse or promote products derived
+ from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGE.
diff --git a/main_func/FISTA_REC.m b/main_func/FISTA_REC.m
new file mode 100644
index 0000000..79369a5
--- /dev/null
+++ b/main_func/FISTA_REC.m
@@ -0,0 +1,338 @@
+function [X, error, objective, residual] = FISTA_REC(params)
+
+% <<<< FISTA-based reconstruction algorithm using ASTRA-toolbox (parallel beam) >>>>
+% ___Input___:
+% params.[] file:
+% - .sino (2D or 3D sinogram) [required]
+% - .N (image dimension) [required]
+% - .angles (in radians) [required]
+% - .iterFISTA (iterations for the main loop)
+% - .L_const (Lipschitz constant, default Power method) )
+% - .X_ideal (ideal image, if given)
+% - .weights (statisitcal weights, size of sinogram)
+% - .ROI (Region-of-interest, only if X_ideal is given)
+% - .lambdaTV (TV regularization parameter, default 0 - reg. TV is switched off)
+% - .tol (tolerance to terminate TV regularization, default 1.0e-04)
+% - .iterTV (iterations for the TV penalty, default 0)
+% - .lambdaHO (Higher Order LLT regularization parameter, default 0 - LLT reg. switched off)
+% - .iterHO (iterations for HO penalty, default 50)
+% - .tauHO (time step parameter for HO term)
+% - .lambdaR_L1 (regularization parameter for L1 ring minimization, if lambdaR_L1 > 0 then switch on ring removal, default 0)
+% - .alpha_ring (larger values can accelerate convergence but check stability, default 1)
+% - .fidelity (choose between "LS" and "student" data fidelities)
+% - .precondition (1 - switch on Fourier filtering before backprojection)
+% - .show (visualize reconstruction 1/0, (0 default))
+% - .maxvalplot (maximum value to use for imshow[0 maxvalplot])
+% - .slice (for 3D volumes - slice number to imshow)
+% ___Output___:
+% 1. X - reconstructed image/volume
+% 2. error - residual error (if X_ideal is given)
+% 3. value of the objective function
+% 4. forward projection(X)
+% References:
+% 1. "A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse
+% Problems" by A. Beck and M Teboulle
+% 2. "Ring artifacts correction in compressed sensing..." by P. Paleo
+% 3. "A novel tomographic reconstruction method based on the robust
+% Student's t function for suppressing data outliers" D. Kazantsev et.al.
+% D. Kazantsev, 2016-17
+
+% Dealing with input parameters
+if (isfield(params,'sino'))
+ sino = params.sino;
+ [anglesNumb, Detectors, SlicesZ] = size(sino);
+ fprintf('%s %i %s %i %s %i %s \n', 'Sinogram has a dimension of', anglesNumb, 'projections;', Detectors, 'detectors;', SlicesZ, 'vertical slices.');
+else
+ fprintf('%s \n', 'Please provide a sinogram');
+end
+if (isfield(params,'N'))
+ N = params.N;
+else
+ fprintf('%s \n', 'Please provide N-size for the reconstructed image [N x N]');
+end
+if (isfield(params,'N'))
+ angles = params.angles;
+ if (length(angles) ~= anglesNumb)
+ fprintf('%s \n', 'Sinogram angular dimension does not correspond to the angles dimension provided');
+ end
+else
+ fprintf('%s \n', 'Please provide a vector of angles');
+end
+if (isfield(params,'iterFISTA'))
+ iterFISTA = params.iterFISTA;
+else
+ iterFISTA = 30;
+end
+if (isfield(params,'L_const'))
+ L_const = params.L_const;
+else
+ % using Power method (PM) to establish L constant
+ vol_geom = astra_create_vol_geom(N, N);
+ proj_geom = astra_create_proj_geom('parallel', 1.0, Detectors, angles);
+
+ niter = 10; % number of iteration for PM
+ x = rand(N,N);
+ [sino_id, y] = astra_create_sino_cuda(x, proj_geom, vol_geom);
+ astra_mex_data2d('delete', sino_id);
+
+ for i = 1:niter
+ x = astra_create_backprojection_cuda(y, proj_geom, vol_geom);
+ s = norm(x);
+ x = x/s;
+ [sino_id, y] = astra_create_sino_cuda(x, proj_geom, vol_geom);
+ astra_mex_data2d('delete', sino_id);
+ end
+ L_const = s;
+end
+if (isfield(params,'X_ideal'))
+ X_ideal = params.X_ideal;
+else
+ X_ideal = 'none';
+end
+if (isfield(params,'weights'))
+ weights = params.weights;
+else
+ weights = 1;
+end
+if (isfield(params,'ROI'))
+ ROI = params.ROI;
+else
+ ROI = find(X_ideal>=0.0);
+end
+if (isfield(params,'lambdaTV'))
+ lambdaTV = params.lambdaTV;
+else
+ lambdaTV = 0;
+end
+if (isfield(params,'tol'))
+ tol = params.tol;
+else
+ tol = 1.0e-04;
+end
+if (isfield(params,'iterTV'))
+ iterTV = params.iterTV;
+else
+ iterTV = 10;
+end
+if (isfield(params,'lambdaHO'))
+ lambdaHO = params.lambdaHO;
+else
+ lambdaHO = 0;
+end
+if (isfield(params,'iterHO'))
+ iterHO = params.iterHO;
+else
+ iterHO = 50;
+end
+if (isfield(params,'tauHO'))
+ tauHO = params.tauHO;
+else
+ tauHO = 0.0001;
+end
+if (isfield(params,'lambdaR_L1'))
+ lambdaR_L1 = params.lambdaR_L1;
+else
+ lambdaR_L1 = 0;
+end
+if (isfield(params,'alpha_ring'))
+ alpha_ring = params.alpha_ring; % higher values can accelerate ring removal procedure
+else
+ alpha_ring = 1;
+end
+if (isfield(params,'fidelity'))
+ fidelity = params.fidelity;
+else
+ fidelity = 'LS';
+end
+if (isfield(params,'precondition'))
+ precondition = params.precondition;
+else
+ precondition = 0;
+end
+if (isfield(params,'show'))
+ show = params.show;
+else
+ show = 0;
+end
+if (isfield(params,'maxvalplot'))
+ maxvalplot = params.maxvalplot;
+else
+ maxvalplot = 1;
+end
+if (isfield(params,'slice'))
+ slice = params.slice;
+else
+ slice = 1;
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% building geometry (parallel-beam)
+vol_geom = astra_create_vol_geom(N, N);
+proj_geom = astra_create_proj_geom('parallel', 1.0, Detectors, angles);
+error = zeros(iterFISTA,1); % error vector
+objective = zeros(iterFISTA,1); % obhective vector
+
+if (lambdaR_L1 > 0)
+ % do reconstruction WITH ring removal (Group-Huber fidelity)
+ t = 1;
+ X = zeros(N,N,SlicesZ, 'single');
+ X_t = X;
+
+ add_ring = zeros(anglesNumb, Detectors, SlicesZ, 'single'); % size of sinogram array
+ r = zeros(Detectors,SlicesZ, 'single'); % 2D array (for 3D data) of sparse "ring" vectors
+ r_x = r;
+
+ % iterations loop
+ for i = 1:iterFISTA
+
+ X_old = X;
+ t_old = t;
+ r_old = r;
+
+ % all slices loop
+ for j = 1:SlicesZ
+
+ [sino_id, sino_updt] = astra_create_sino_cuda(X_t(:,:,j), proj_geom, vol_geom);
+
+ for kkk = 1:anglesNumb
+ add_ring(kkk,:,j) = sino(kkk,:,j) - alpha_ring.*r_x(:,j)';
+ end
+
+ residual = sino_updt - add_ring(:,:,j);
+
+ if (precondition == 1)
+ residual = filtersinc(residual'); % filtering residual (Fourier preconditioning)
+ residual = residual';
+ end
+
+ vec = sum(residual);
+ r(:,j) = r_x(:,j) - (1/L_const).*vec';
+
+ x_temp = astra_create_backprojection_cuda(residual, proj_geom, vol_geom);
+
+ X(:,:,j) = X_t(:,:,j) - (1/L_const).*x_temp;
+ astra_mex_data2d('delete', sino_id);
+ end
+
+ if ((lambdaTV > 0) && (lambdaHO == 0))
+ if (size(X,3) > 1)
+ [X] = FISTA_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA
+ gradTV = 1;
+ else
+ [X, gradTV] = FISTA_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA
+ end
+ objective(i) = 0.5.*norm(residual(:))^2 + norm(gradTV(:));
+ % X = SplitBregman_TV(single(X), lambdaTV, iterTV, tol); % TV-Split Bregman regularization on CPU (memory limited)
+ elseif ((lambdaHO > 0) && (lambdaTV == 0))
+ % Higher Order regularization
+ X = LLT_model(single(X), lambdaHO, tauHO, iterHO, tol, 0); % LLT higher order model
+ elseif ((lambdaTV > 0) && (lambdaHO > 0))
+ %X1 = SplitBregman_TV(single(X), lambdaTV, iterTV, tol); % TV-Split Bregman regularization on CPU (memory limited)
+ X1 = FISTA_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA
+ X2 = LLT_model(single(X), lambdaHO, tauHO, iterHO, tol, 0); % LLT higher order model
+ X = 0.5.*(X1 + X2); % averaged combination of two solutions
+ elseif ((lambdaTV == 0) && (lambdaHO == 0))
+ objective(i) = 0.5.*norm(residual(:))^2;
+ end
+
+ r = max(abs(r)-lambdaR_L1, 0).*sign(r); % soft-thresholding operator
+
+ t = (1 + sqrt(1 + 4*t^2))/2; % updating t
+ X_t = X + ((t_old-1)/t).*(X - X_old); % updating X
+ r_x = r + ((t_old-1)/t).*(r - r_old); % updating r
+
+ if (show == 1)
+ figure(10); imshow(X(:,:,slice), [0 maxvalplot]);
+ figure(11); plot(r); title('Rings offset vector')
+ pause(0.03);
+ end
+ if (strcmp(X_ideal, 'none' ) == 0)
+ error(i) = RMSE(X(ROI), X_ideal(ROI));
+ fprintf('%s %i %s %s %.4f %s %s %.4f \n', 'Iteration Number:', i, '|', 'Error RMSE:', error(i), '|', 'Objective:', objective(i));
+ else
+ fprintf('%s %i %s %s %.4f \n', 'Iteration Number:', i, '|', 'Objective:', objective(i));
+ end
+
+ end
+
+else
+ % WITHOUT ring removal
+ t = 1;
+ X = zeros(N,N,SlicesZ, 'single');
+ X_t = X;
+
+ % iterations loop
+ for i = 1:iterFISTA
+
+ X_old = X;
+ t_old = t;
+
+ % slices loop
+ for j = 1:SlicesZ
+ [sino_id, sino_updt] = astra_create_sino_cuda(X_t(:,:,j), proj_geom, vol_geom);
+ residual = weights.*(sino_updt - sino(:,:,j));
+
+ % employ students t fidelity term
+ if (strcmp(fidelity,'student') == 1)
+ res_vec = reshape(residual, anglesNumb*Detectors,1);
+ %s = 100;
+ %gr = (2)*res_vec./(s*2 + conj(res_vec).*res_vec);
+ [ff, gr] = studentst(res_vec,1);
+ residual = reshape(gr, anglesNumb, Detectors);
+ end
+
+ if (precondition == 1)
+ residual = filtersinc(residual'); % filtering residual (Fourier preconditioning)
+ residual = residual';
+ end
+
+ x_temp = astra_create_backprojection_cuda(residual, proj_geom, vol_geom);
+ X(:,:,j) = X_t(:,:,j) - (1/L_const).*x_temp;
+ astra_mex_data2d('delete', sino_id);
+ end
+
+ if ((lambdaTV > 0) && (lambdaHO == 0))
+ if (size(X,3) > 1)
+ [X] = FISTA_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA
+ gradTV = 1;
+ else
+ [X, gradTV] = FISTA_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA
+ end
+ if (strcmp(fidelity,'student') == 1)
+ objective(i) = ff + norm(gradTV(:));
+ else
+ objective(i) = 0.5.*norm(residual(:))^2 + norm(gradTV(:));
+ end
+ % X = SplitBregman_TV(single(X), lambdaTV, iterTV, tol); % TV-Split Bregman regularization on CPU (memory limited)
+ elseif ((lambdaHO > 0) && (lambdaTV == 0))
+ % Higher Order regularization
+ X = LLT_model(single(X), lambdaHO, tauHO, iterHO, tol, 0); % LLT higher order model
+ elseif ((lambdaTV > 0) && (lambdaHO > 0))
+ X1 = SplitBregman_TV(single(X), lambdaTV, iterTV, tol); % TV-Split Bregman regularization on CPU (memory limited)
+ X2 = LLT_model(single(X), lambdaHO, tauHO, iterHO, tol, 0); % LLT higher order model
+ X = 0.5.*(X1 + X2); % averaged combination of two solutions
+ elseif ((lambdaTV == 0) && (lambdaHO == 0))
+ objective(i) = 0.5.*norm(residual(:))^2;
+ end
+
+
+ t = (1 + sqrt(1 + 4*t^2))/2; % updating t
+ X_t = X + ((t_old-1)/t).*(X - X_old); % updating X
+
+ if (show == 1)
+ figure(11); imshow(X(:,:,slice), [0 maxvalplot]);
+ pause(0.03);
+ end
+ if (strcmp(X_ideal, 'none' ) == 0)
+ error(i) = RMSE(X(ROI), X_ideal(ROI));
+ fprintf('%s %i %s %s %.4f %s %s %.4f \n', 'Iteration Number:', i, '|', 'Error RMSE:', error(i), '|', 'Objective:', objective(i));
+ else
+ fprintf('%s %i %s %s %.4f \n', 'Iteration Number:', i, '|', 'Objective:', objective(i));
+ end
+
+
+ end
+
+end
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+end
diff --git a/main_func/FISTA_TV.c b/main_func/FISTA_TV.c
new file mode 100644
index 0000000..87681bc
--- /dev/null
+++ b/main_func/FISTA_TV.c
@@ -0,0 +1,331 @@
+#include "mex.h"
+#include <matrix.h>
+#include <math.h>
+#include <stdlib.h>
+#include <memory.h>
+#include <stdio.h>
+#include "omp.h"
+
+/* C-OMP implementation of FISTA-TV denoising-regularization model (2D/3D)
+ *
+ * Input Parameters:
+ * 1. Noisy image/volume
+ * 2. lambda - regularization parameter
+ * 3. Number of iterations
+ * 4. eplsilon - tolerance constant
+ *
+ * Output:
+ * Filtered/regularized image
+ *
+ * Example:
+ * figure;
+ * Im = double(imread('lena_gray_256.tif'))/255; % loading image
+ * u0 = Im + .05*randn(size(Im)); % adding noise
+ * u = FISTA_TV(single(u0), 0.05, 150, 1e-04);
+ *
+ * to compile with OMP support: mex FISTA_TV.c CFLAGS="\$CFLAGS -fopenmp -Wall" LDFLAGS="\$LDFLAGS -fopenmp"
+ * References: A. Beck & M. Teboulle
+ *
+ * D. Kazantsev, 2016*
+ */
+
+float copyIm(float *A, float *B, int dimX, int dimY, int dimZ);
+float Obj_func2D(float *A, float *D, float *R1, float *R2, float *grad, float lambda, int dimX, int dimY);
+float Grad_func2D(float *P1, float *P2, float *D, float *R1, float *R2, float lambda, int dimX, int dimY);
+float Proj_func2D(float *P1, float *P2, int dimX, int dimY);
+float Rupd_func2D(float *P1, float *P1_old, float *P2, float *P2_old, float *R1, float *R2, float tkp1, float tk, int dimX, int dimY);
+
+float Obj_func3D(float *A, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ);
+float Grad_func3D(float *P1, float *P2, float *P3, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ);
+float Proj_func3D(float *P1, float *P2, float *P3, int dimX, int dimY, int dimZ);
+float Rupd_func3D(float *P1, float *P1_old, float *P2, float *P2_old, float *P3, float *P3_old, float *R1, float *R2, float *R3, float tkp1, float tk, int dimX, int dimY, int dimZ);
+
+
+void mexFunction(
+ int nlhs, mxArray *plhs[],
+ int nrhs, const mxArray *prhs[])
+
+{
+ int number_of_dims, iter, dimX, dimY, dimZ, ll, j, count;
+ const int *dim_array;
+ float *A, *grad=NULL, *D=NULL, *D_old=NULL, *P1=NULL, *P2=NULL, *P3=NULL, *P1_old=NULL, *P2_old=NULL, *P3_old=NULL, *R1=NULL, *R2=NULL, *R3=NULL, lambda, tk, tkp1, re, re1, re_old, epsil;
+
+ number_of_dims = mxGetNumberOfDimensions(prhs[0]);
+ dim_array = mxGetDimensions(prhs[0]);
+
+ if(nrhs != 4) mexErrMsgTxt("Four input parameters is reqired: Image(2D/3D), Regularization parameter, Iterations, Tolerance");
+
+ /*Handling Matlab input data*/
+ A = (float *) mxGetData(prhs[0]); /*noisy image (2D/3D) */
+ lambda = (float) mxGetScalar(prhs[1]); /* regularization parameter */
+ iter = (int) mxGetScalar(prhs[2]); /* iterations number */
+ epsil = (float) mxGetScalar(prhs[3]); /* tolerance constant */
+
+ /*Handling Matlab output data*/
+ dimX = dim_array[0]; dimY = dim_array[1]; dimZ = dim_array[2];
+
+ tk = 1.0f;
+ tkp1=1.0f;
+ count = 1;
+ re_old = 0.0f;
+
+ if (number_of_dims == 2) {
+ dimZ = 1; /*2D case*/
+ D = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ grad = (float*)mxGetPr(plhs[1] = mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ D_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ P1 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ P2 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ P1_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ P2_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ R1 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ R2 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+
+ /* begin iterations */
+ for(ll=0; ll<iter; ll++) {
+
+ /*storing old values*/
+ copyIm(D, D_old, dimX, dimY, dimZ);
+ copyIm(P1, P1_old, dimX, dimY, dimZ);
+ copyIm(P2, P2_old, dimX, dimY, dimZ);
+ tk = tkp1;
+
+ /* computing the gradient of the objective function */
+ Obj_func2D(A, D, R1, R2, grad, lambda, dimX, dimY);
+
+ /*Taking a step towards minus of the gradient*/
+ Grad_func2D(P1, P2, D, R1, R2, lambda, dimX, dimY);
+
+ /* projection step */
+ Proj_func2D(P1, P2, dimX, dimY);
+
+ /*updating R and t*/
+ tkp1 = (1.0f + sqrt(1.0f + 4.0f*tk*tk))*0.5f;
+ Rupd_func2D(P1, P1_old, P2, P2_old, R1, R2, tkp1, tk, dimX, dimY);
+
+ /* calculate norm */
+ re = 0.0f; re1 = 0.0f;
+ for(j=0; j<dimX*dimY*dimZ; j++)
+ {
+ re += pow(D[j] - D_old[j],2);
+ re1 += pow(D[j],2);
+ }
+ re = sqrt(re)/sqrt(re1);
+ if (re < epsil) count++;
+ if (count > 3) break;
+
+ /* check that the residual norm is decreasing */
+ if (ll > 2) {
+ if (re > re_old) break; }
+
+ re_old = re;
+ /*printf("%f %i %i \n", re, ll, count); */
+ }
+ printf("TV iterations stopped at iteration: %i\n", ll);
+ }
+ if (number_of_dims == 3) {
+ D = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ D_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ P1 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ P2 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ P3 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ P1_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ P2_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ P3_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ R1 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ R2 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ R3 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+
+ /* begin iterations */
+ for(ll=0; ll<iter; ll++) {
+
+ /*storing old values*/
+ copyIm(D, D_old, dimX, dimY, dimZ);
+ copyIm(P1, P1_old, dimX, dimY, dimZ);
+ copyIm(P2, P2_old, dimX, dimY, dimZ);
+ copyIm(P3, P3_old, dimX, dimY, dimZ);
+
+ tk = tkp1;
+
+ /* computing the gradient of the objective function */
+ Obj_func3D(A, D, R1, R2, R3,lambda, dimX, dimY, dimZ);
+
+ /*Taking a step towards minus of the gradient*/
+ Grad_func3D(P1, P2, P3, D, R1, R2, R3, lambda, dimX, dimY, dimZ);
+
+ /* projection step */
+ Proj_func3D(P1, P2, P3, dimX, dimY, dimZ);
+
+ /*updating R and t*/
+ tkp1 = (1.0f + sqrt(1.0f + 4.0f*tk*tk))*0.5f;
+ Rupd_func3D(P1, P1_old, P2, P2_old, P3, P3_old, R1, R2, R3, tkp1, tk, dimX, dimY, dimZ);
+
+ /* calculate norm - stopping rules*/
+ re = 0.0f; re1 = 0.0f;
+ for(j=0; j<dimX*dimY*dimZ; j++)
+ {
+ re += pow(D[j] - D_old[j],2);
+ re1 += pow(D[j],2);
+ }
+ re = sqrt(re)/sqrt(re1);
+ /* stop if the norm residual is less than the tolerance EPS */
+ if (re < epsil) count++;
+ if (count > 3) break;
+
+ /* check that the residual norm is decreasing */
+ if (ll > 2) {
+ if (re > re_old) break; }
+
+ re_old = re;
+ /*printf("%f %i %i \n", re, ll, count); */
+ }
+ printf("TV iterations stopped at iteration: %i\n", ll);
+ }
+}
+
+/* 2D-case related Functions */
+/*****************************************************************/
+float Obj_func2D(float *A, float *D, float *R1, float *R2, float *grad, float lambda, int dimX, int dimY)
+{
+ float val1, val2;
+ int i,j;
+#pragma omp parallel for shared(A,D,R1,R2) private(i,j,val1,val2)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ /* symmetric boundary conditions (Neuman) */
+ if (i == 0) {val1 = R1[(i+1)*dimY + (j)];} else {val1 = R1[(i-1)*dimY + (j)];}
+ if (j == 0) {val2 = R2[(i)*dimY + (j+1)];} else {val2 = R2[(i)*dimY + (j-1)];}
+ D[(i)*dimY + (j)] = A[(i)*dimY + (j)] - lambda*(R1[(i)*dimY + (j)] + R2[(i)*dimY + (j)] - val1 - val2);
+ grad[(i)*dimY + (j)] = lambda*(R1[(i)*dimY + (j)] + R2[(i)*dimY + (j)] - val1 - val2);
+ }}
+ return *D;
+}
+float Grad_func2D(float *P1, float *P2, float *D, float *R1, float *R2, float lambda, int dimX, int dimY)
+{
+ float val1, val2;
+ int i,j;
+#pragma omp parallel for shared(P1,P2,D,R1,R2) private(i,j,val1,val2)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ /* symmetric boundary conditions (Neuman) */
+
+ if (i == dimX-1) {val1 = D[(i)*dimY + (j)] - D[(i-1)*dimY + (j)];} else {val1 = D[(i)*dimY + (j)] - D[(i+1)*dimY + (j)];}
+ if (j == dimY-1) {val2 = D[(i)*dimY + (j)] - D[(i)*dimY + (j-1)];} else {val2 = D[(i)*dimY + (j)] - D[(i)*dimY + (j+1)];}
+
+ P1[(i)*dimY + (j)] = R1[(i)*dimY + (j)] + (1.0f/(8.0f*lambda))*val1;
+ P2[(i)*dimY + (j)] = R2[(i)*dimY + (j)] + (1.0f/(8.0f*lambda))*val2;
+ }}
+ return 1;
+}
+float Proj_func2D(float *P1, float *P2, int dimX, int dimY)
+{
+ float val1, val2;
+ int i,j;
+#pragma omp parallel for shared(P1,P2) private(i,j,val1,val2)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ val1 = fabs(P1[(i)*dimY + (j)]);
+ val2 = fabs(P2[(i)*dimY + (j)]);
+ if (val1 < 1.0f) {val1 = 1.0f;}
+ if (val2 < 1.0f) {val2 = 1.0f;}
+
+ P1[(i)*dimY + (j)] = P1[(i)*dimY + (j)]/val1;
+ P2[(i)*dimY + (j)] = P2[(i)*dimY + (j)]/val2;
+ }}
+ return 1;
+}
+float Rupd_func2D(float *P1, float *P1_old, float *P2, float *P2_old, float *R1, float *R2, float tkp1, float tk, int dimX, int dimY)
+{
+ int i,j;
+#pragma omp parallel for shared(P1,P2,P1_old,P2_old,R1,R2) private(i,j)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ R1[(i)*dimY + (j)] = P1[(i)*dimY + (j)] + ((tk-1.0f)/tkp1)*(P1[(i)*dimY + (j)] - P1_old[(i)*dimY + (j)]);
+ R2[(i)*dimY + (j)] = P2[(i)*dimY + (j)] + ((tk-1.0f)/tkp1)*(P2[(i)*dimY + (j)] - P2_old[(i)*dimY + (j)]);
+ }}
+ return 1;
+}
+
+
+/* 3D-case related Functions */
+/*****************************************************************/
+float Obj_func3D(float *A, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ)
+{
+ float val1, val2, val3;
+ int i,j,k;
+#pragma omp parallel for shared(A,D,R1,R2,R3) private(i,j,k,val1,val2,val3)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ for(k=0; k<dimZ; k++) {
+ /* symmetric boundary conditions (Neuman) */
+ if (i == 0) {val1 = R1[(dimX*dimY)*k + (i+1)*dimY + (j)];} else {val1 = R1[(dimX*dimY)*k + (i-1)*dimY + (j)];}
+ if (j == 0) {val2 = R2[(dimX*dimY)*k + (i)*dimY + (j+1)];} else {val2 = R2[(dimX*dimY)*k + (i)*dimY + (j-1)];}
+ if (k == 0) {val3 = R3[(dimX*dimY)*(k+1) + (i)*dimY + (j)];} else {val3 = R3[(dimX*dimY)*(k-1) + (i)*dimY + (j)];}
+ D[(dimX*dimY)*k + (i)*dimY + (j)] = A[(dimX*dimY)*k + (i)*dimY + (j)] - lambda*(R1[(dimX*dimY)*k + (i)*dimY + (j)] + R2[(dimX*dimY)*k + (i)*dimY + (j)] + R3[(dimX*dimY)*k + (i)*dimY + (j)] - val1 - val2 - val3);
+ }}}
+ return *D;
+}
+float Grad_func3D(float *P1, float *P2, float *P3, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ)
+{
+ float val1, val2, val3;
+ int i,j,k;
+#pragma omp parallel for shared(P1,P2,P3,D,R1,R2,R3) private(i,j,k,val1,val2,val3)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ for(k=0; k<dimZ; k++) {
+ /* symmetric boundary conditions (Neuman) */
+ if (i == dimX-1) {val1 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*k + (i-1)*dimY + (j)];} else {val1 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*k + (i+1)*dimY + (j)];}
+ if (j == dimY-1) {val2 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*k + (i)*dimY + (j-1)];} else {val2 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*k + (i)*dimY + (j+1)];}
+ if (k == dimZ-1) {val3 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*(k-1) + (i)*dimY + (j)];} else {val3 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*(k+1) + (i)*dimY + (j)];}
+
+ P1[(dimX*dimY)*k + (i)*dimY + (j)] = R1[(dimX*dimY)*k + (i)*dimY + (j)] + (1.0f/(8.0f*lambda))*val1;
+ P2[(dimX*dimY)*k + (i)*dimY + (j)] = R2[(dimX*dimY)*k + (i)*dimY + (j)] + (1.0f/(8.0f*lambda))*val2;
+ P3[(dimX*dimY)*k + (i)*dimY + (j)] = R3[(dimX*dimY)*k + (i)*dimY + (j)] + (1.0f/(8.0f*lambda))*val3;
+ }}}
+ return 1;
+}
+float Proj_func3D(float *P1, float *P2, float *P3, int dimX, int dimY, int dimZ)
+{
+ float val1, val2, val3;
+ int i,j,k;
+#pragma omp parallel for shared(P1,P2,P3) private(i,j,k,val1,val2,val3)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ for(k=0; k<dimZ; k++) {
+ val1 = fabs(P1[(dimX*dimY)*k + (i)*dimY + (j)]);
+ val2 = fabs(P2[(dimX*dimY)*k + (i)*dimY + (j)]);
+ val3 = fabs(P3[(dimX*dimY)*k + (i)*dimY + (j)]);
+ if (val1 < 1.0f) {val1 = 1.0f;}
+ if (val2 < 1.0f) {val2 = 1.0f;}
+ if (val3 < 1.0f) {val3 = 1.0f;}
+
+ P1[(dimX*dimY)*k + (i)*dimY + (j)] = P1[(dimX*dimY)*k + (i)*dimY + (j)]/val1;
+ P2[(dimX*dimY)*k + (i)*dimY + (j)] = P2[(dimX*dimY)*k + (i)*dimY + (j)]/val2;
+ P3[(dimX*dimY)*k + (i)*dimY + (j)] = P3[(dimX*dimY)*k + (i)*dimY + (j)]/val3;
+ }}}
+ return 1;
+}
+float Rupd_func3D(float *P1, float *P1_old, float *P2, float *P2_old, float *P3, float *P3_old, float *R1, float *R2, float *R3, float tkp1, float tk, int dimX, int dimY, int dimZ)
+{
+ int i,j,k;
+#pragma omp parallel for shared(P1,P2,P3,P1_old,P2_old,P3_old,R1,R2,R3) private(i,j,k)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ for(k=0; k<dimZ; k++) {
+ R1[(dimX*dimY)*k + (i)*dimY + (j)] = P1[(dimX*dimY)*k + (i)*dimY + (j)] + ((tk-1.0f)/tkp1)*(P1[(dimX*dimY)*k + (i)*dimY + (j)] - P1_old[(dimX*dimY)*k + (i)*dimY + (j)]);
+ R2[(dimX*dimY)*k + (i)*dimY + (j)] = P2[(dimX*dimY)*k + (i)*dimY + (j)] + ((tk-1.0f)/tkp1)*(P2[(dimX*dimY)*k + (i)*dimY + (j)] - P2_old[(dimX*dimY)*k + (i)*dimY + (j)]);
+ R3[(dimX*dimY)*k + (i)*dimY + (j)] = P3[(dimX*dimY)*k + (i)*dimY + (j)] + ((tk-1.0f)/tkp1)*(P3[(dimX*dimY)*k + (i)*dimY + (j)] - P3_old[(dimX*dimY)*k + (i)*dimY + (j)]);
+ }}}
+ return 1;
+}
+
+/* General Functions */
+/*****************************************************************/
+/* Copy Image */
+float copyIm(float *A, float *B, int dimX, int dimY, int dimZ)
+{
+ int j;
+#pragma omp parallel for shared(A, B) private(j)
+ for(j=0; j<dimX*dimY*dimZ; j++) B[j] = A[j];
+ return *B;
+} \ No newline at end of file
diff --git a/main_func/LLT_model.c b/main_func/LLT_model.c
new file mode 100644
index 0000000..a611e54
--- /dev/null
+++ b/main_func/LLT_model.c
@@ -0,0 +1,431 @@
+#include "mex.h"
+#include <matrix.h>
+#include <math.h>
+#include <stdlib.h>
+#include <memory.h>
+#include <stdio.h>
+#include "omp.h"
+
+#define EPS 0.001
+
+/* C-OMP implementation of Lysaker, Lundervold and Tai (LLT) model of higher order regularization penalty
+ *
+ * Input Parameters:
+ * 1. U0 - origanal noise image/volume
+ * 2. lambda - regularization parameter
+ * 3. tau - time-step for explicit scheme
+ * 4. iter - iterations number
+ * 5. epsil - tolerance constant (to terminate earlier)
+ * 6. switcher - default is 0, switch to (1) to restrictive smoothing in Z dimension (in test)
+ *
+ * Output:
+ * Filtered/regularized image
+ *
+ * Example:
+ * figure;
+ * Im = double(imread('lena_gray_256.tif'))/255; % loading image
+ * u0 = Im + .03*randn(size(Im)); % adding noise
+ * [Den] = LLT_model(single(u0), 10, 0.1, 1);
+ *
+ *
+ * to compile with OMP support: mex LLT_model.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp"
+ * References: Lysaker, Lundervold and Tai (LLT) 2003, IEEE
+ *
+ * 28.11.16/Harwell
+ */
+/* 2D functions */
+float der2D(float *U, float *D1, float *D2, int dimX, int dimY, int dimZ);
+float div_upd2D(float *U0, float *U, float *D1, float *D2, int dimX, int dimY, int dimZ, float lambda, float tau);
+
+float der3D(float *U, float *D1, float *D2, float *D3, int dimX, int dimY, int dimZ);
+float div_upd3D(float *U0, float *U, float *D1, float *D2, float *D3, unsigned short *Map, int switcher, int dimX, int dimY, int dimZ, float lambda, float tau);
+
+float calcMap(float *U, unsigned short *Map, int dimX, int dimY, int dimZ);
+float cleanMap(unsigned short *Map, int dimX, int dimY, int dimZ);
+
+float copyIm(float *A, float *U, int dimX, int dimY, int dimZ);
+
+void mexFunction(
+ int nlhs, mxArray *plhs[],
+ int nrhs, const mxArray *prhs[])
+
+{
+ int number_of_dims, iter, dimX, dimY, dimZ, ll, j, count, switcher;
+ const int *dim_array;
+ float *U0, *U=NULL, *U_old=NULL, *D1=NULL, *D2=NULL, *D3=NULL, lambda, tau, re, re1, epsil, re_old;
+ unsigned short *Map=NULL;
+
+ number_of_dims = mxGetNumberOfDimensions(prhs[0]);
+ dim_array = mxGetDimensions(prhs[0]);
+
+ /*Handling Matlab input data*/
+ U0 = (float *) mxGetData(prhs[0]); /*origanal noise image/volume*/
+ if (mxGetClassID(prhs[0]) != mxSINGLE_CLASS) {mexErrMsgTxt("The input in single precision is required"); }
+ lambda = (float) mxGetScalar(prhs[1]); /*regularization parameter*/
+ tau = (float) mxGetScalar(prhs[2]); /* time-step */
+ iter = (int) mxGetScalar(prhs[3]); /*iterations number*/
+ epsil = (float) mxGetScalar(prhs[4]); /* tolerance constant */
+ switcher = (int) mxGetScalar(prhs[5]); /*switch on (1) restrictive smoothing in Z dimension*/
+
+ /*Handling Matlab output data*/
+ dimX = dim_array[0]; dimY = dim_array[1]; dimZ = 1;
+
+ if (number_of_dims == 2) {
+ /*2D case*/
+ U = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ U_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ D1 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ D2 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ }
+ else if (number_of_dims == 3) {
+ /*3D case*/
+ dimZ = dim_array[2];
+ U = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ U_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ D1 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ D2 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ D3 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ if (switcher != 0) {
+ Map = (unsigned short*)mxGetPr(plhs[1] = mxCreateNumericArray(3, dim_array, mxUINT16_CLASS, mxREAL));
+ }
+ }
+ else {mexErrMsgTxt("The input data should be 2D or 3D");}
+
+ /*Copy U0 to U*/
+ copyIm(U0, U, dimX, dimY, dimZ);
+
+ count = 1;
+ re_old = 0.0f;
+ if (number_of_dims == 2) {
+ for(ll = 0; ll < iter; ll++) {
+
+ copyIm(U, U_old, dimX, dimY, dimZ);
+
+ /*estimate inner derrivatives */
+ der2D(U, D1, D2, dimX, dimY, dimZ);
+ /* calculate div^2 and update */
+ div_upd2D(U0, U, D1, D2, dimX, dimY, dimZ, lambda, tau);
+
+ /* calculate norm to terminate earlier */
+ re = 0.0f; re1 = 0.0f;
+ for(j=0; j<dimX*dimY*dimZ; j++)
+ {
+ re += pow(U_old[j] - U[j],2);
+ re1 += pow(U_old[j],2);
+ }
+ re = sqrt(re)/sqrt(re1);
+ if (re < epsil) count++;
+ if (count > 4) break;
+
+ /* check that the residual norm is decreasing */
+ if (ll > 2) {
+ if (re > re_old) break;
+ }
+ re_old = re;
+
+ } /*end of iterations*/
+ printf("HO iterations stopped at iteration: %i\n", ll);
+ }
+ /*3D version*/
+ if (number_of_dims == 3) {
+
+ if (switcher == 1) {
+ /* apply restrictive smoothing */
+ calcMap(U, Map, dimX, dimY, dimZ);
+ /*clear outliers */
+ cleanMap(Map, dimX, dimY, dimZ);
+ }
+ for(ll = 0; ll < iter; ll++) {
+
+ copyIm(U, U_old, dimX, dimY, dimZ);
+
+ /*estimate inner derrivatives */
+ der3D(U, D1, D2, D3, dimX, dimY, dimZ);
+ /* calculate div^2 and update */
+ div_upd3D(U0, U, D1, D2, D3, Map, switcher, dimX, dimY, dimZ, lambda, tau);
+
+ /* calculate norm to terminate earlier */
+ re = 0.0f; re1 = 0.0f;
+ for(j=0; j<dimX*dimY*dimZ; j++)
+ {
+ re += pow(U_old[j] - U[j],2);
+ re1 += pow(U_old[j],2);
+ }
+ re = sqrt(re)/sqrt(re1);
+ if (re < epsil) count++;
+ if (count > 4) break;
+
+ /* check that the residual norm is decreasing */
+ if (ll > 2) {
+ if (re > re_old) break;
+ }
+ re_old = re;
+
+ } /*end of iterations*/
+ printf("HO iterations stopped at iteration: %i\n", ll);
+ }
+}
+
+float der2D(float *U, float *D1, float *D2, int dimX, int dimY, int dimZ)
+{
+ int i, j, i_p, i_m, j_m, j_p;
+ float dxx, dyy, denom_xx, denom_yy;
+#pragma omp parallel for shared(U,D1,D2) private(i, j, i_p, i_m, j_m, j_p, denom_xx, denom_yy, dxx, dyy)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ /* symmetric boundary conditions (Neuman) */
+ i_p = i + 1; if (i_p == dimX) i_p = i - 1;
+ i_m = i - 1; if (i_m < 0) i_m = i + 1;
+ j_p = j + 1; if (j_p == dimY) j_p = j - 1;
+ j_m = j - 1; if (j_m < 0) j_m = j + 1;
+
+ dxx = U[i_p*dimY + j] - 2.0f*U[i*dimY + j] + U[i_m*dimY + j];
+ dyy = U[i*dimY + j_p] - 2.0f*U[i*dimY + j] + U[i*dimY + j_m];
+
+ denom_xx = fabs(dxx) + EPS;
+ denom_yy = fabs(dyy) + EPS;
+
+ D1[i*dimY + j] = dxx/denom_xx;
+ D2[i*dimY + j] = dyy/denom_yy;
+ }}
+ return 1;
+}
+float div_upd2D(float *U0, float *U, float *D1, float *D2, int dimX, int dimY, int dimZ, float lambda, float tau)
+{
+ int i, j, i_p, i_m, j_m, j_p;
+ float div, dxx, dyy;
+#pragma omp parallel for shared(U,U0,D1,D2) private(i, j, i_p, i_m, j_m, j_p, div, dxx, dyy)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ /* symmetric boundary conditions (Neuman) */
+ i_p = i + 1; if (i_p == dimX) i_p = i - 1;
+ i_m = i - 1; if (i_m < 0) i_m = i + 1;
+ j_p = j + 1; if (j_p == dimY) j_p = j - 1;
+ j_m = j - 1; if (j_m < 0) j_m = j + 1;
+
+ dxx = D1[i_p*dimY + j] - 2.0f*D1[i*dimY + j] + D1[i_m*dimY + j];
+ dyy = D2[i*dimY + j_p] - 2.0f*D2[i*dimY + j] + D2[i*dimY + j_m];
+
+ div = dxx + dyy;
+
+ U[i*dimY + j] = U[i*dimY + j] - tau*div - tau*lambda*(U[i*dimY + j] - U0[i*dimY + j]);
+ }}
+ return *U0;
+}
+
+float der3D(float *U, float *D1, float *D2, float *D3, int dimX, int dimY, int dimZ)
+{
+ int i, j, k, i_p, i_m, j_m, j_p, k_p, k_m;
+ float dxx, dyy, dzz, denom_xx, denom_yy, denom_zz;
+#pragma omp parallel for shared(U,D1,D2,D3) private(i, j, k, i_p, i_m, j_m, j_p, k_p, k_m, denom_xx, denom_yy, denom_zz, dxx, dyy, dzz)
+ for(i=0; i<dimX; i++) {
+ /* symmetric boundary conditions (Neuman) */
+ i_p = i + 1; if (i_p == dimX) i_p = i - 1;
+ i_m = i - 1; if (i_m < 0) i_m = i + 1;
+ for(j=0; j<dimY; j++) {
+ j_p = j + 1; if (j_p == dimY) j_p = j - 1;
+ j_m = j - 1; if (j_m < 0) j_m = j + 1;
+ for(k=0; k<dimZ; k++) {
+ k_p = k + 1; if (k_p == dimZ) k_p = k - 1;
+ k_m = k - 1; if (k_m < 0) k_m = k + 1;
+
+ dxx = U[dimX*dimY*k + i_p*dimY + j] - 2.0f*U[dimX*dimY*k + i*dimY + j] + U[dimX*dimY*k + i_m*dimY + j];
+ dyy = U[dimX*dimY*k + i*dimY + j_p] - 2.0f*U[dimX*dimY*k + i*dimY + j] + U[dimX*dimY*k + i*dimY + j_m];
+ dzz = U[dimX*dimY*k_p + i*dimY + j] - 2.0f*U[dimX*dimY*k + i*dimY + j] + U[dimX*dimY*k_m + i*dimY + j];
+
+ denom_xx = fabs(dxx) + EPS;
+ denom_yy = fabs(dyy) + EPS;
+ denom_zz = fabs(dzz) + EPS;
+
+ D1[dimX*dimY*k + i*dimY + j] = dxx/denom_xx;
+ D2[dimX*dimY*k + i*dimY + j] = dyy/denom_yy;
+ D3[dimX*dimY*k + i*dimY + j] = dzz/denom_zz;
+
+ }}}
+ return 1;
+}
+
+float div_upd3D(float *U0, float *U, float *D1, float *D2, float *D3, unsigned short *Map, int switcher, int dimX, int dimY, int dimZ, float lambda, float tau)
+{
+ int i, j, k, i_p, i_m, j_m, j_p, k_p, k_m;
+ float div, dxx, dyy, dzz;
+#pragma omp parallel for shared(U,U0,D1,D2,D3) private(i, j, k, i_p, i_m, j_m, j_p, k_p, k_m, div, dxx, dyy, dzz)
+ for(i=0; i<dimX; i++) {
+ /* symmetric boundary conditions (Neuman) */
+ i_p = i + 1; if (i_p == dimX) i_p = i - 1;
+ i_m = i - 1; if (i_m < 0) i_m = i + 1;
+ for(j=0; j<dimY; j++) {
+ j_p = j + 1; if (j_p == dimY) j_p = j - 1;
+ j_m = j - 1; if (j_m < 0) j_m = j + 1;
+ for(k=0; k<dimZ; k++) {
+ k_p = k + 1; if (k_p == dimZ) k_p = k - 1;
+ k_m = k - 1; if (k_m < 0) k_m = k + 1;
+// k_p1 = k + 2; if (k_p1 >= dimZ) k_p1 = k - 2;
+// k_m1 = k - 2; if (k_m1 < 0) k_m1 = k + 2;
+
+ dxx = D1[dimX*dimY*k + i_p*dimY + j] - 2.0f*D1[dimX*dimY*k + i*dimY + j] + D1[dimX*dimY*k + i_m*dimY + j];
+ dyy = D2[dimX*dimY*k + i*dimY + j_p] - 2.0f*D2[dimX*dimY*k + i*dimY + j] + D2[dimX*dimY*k + i*dimY + j_m];
+ dzz = D3[dimX*dimY*k_p + i*dimY + j] - 2.0f*D3[dimX*dimY*k + i*dimY + j] + D3[dimX*dimY*k_m + i*dimY + j];
+
+ if ((switcher == 1) && (Map[dimX*dimY*k + i*dimY + j] == 0)) dzz = 0;
+ div = dxx + dyy + dzz;
+
+// if (switcher == 1) {
+ // if (Map2[dimX*dimY*k + i*dimY + j] == 0) dzz2 = 0;
+ //else dzz2 = D4[dimX*dimY*k_p1 + i*dimY + j] - 2.0f*D4[dimX*dimY*k + i*dimY + j] + D4[dimX*dimY*k_m1 + i*dimY + j];
+// div = dzz + dzz2;
+// }
+
+// dzz = D3[dimX*dimY*k_p + i*dimY + j] - 2.0f*D3[dimX*dimY*k + i*dimY + j] + D3[dimX*dimY*k_m + i*dimY + j];
+// dzz2 = D4[dimX*dimY*k_p1 + i*dimY + j] - 2.0f*D4[dimX*dimY*k + i*dimY + j] + D4[dimX*dimY*k_m1 + i*dimY + j];
+// div = dzz + dzz2;
+
+ U[dimX*dimY*k + i*dimY + j] = U[dimX*dimY*k + i*dimY + j] - tau*div - tau*lambda*(U[dimX*dimY*k + i*dimY + j] - U0[dimX*dimY*k + i*dimY + j]);
+ }}}
+ return *U0;
+ }
+
+// float der3D_2(float *U, float *D1, float *D2, float *D3, float *D4, int dimX, int dimY, int dimZ)
+// {
+// int i, j, k, i_p, i_m, j_m, j_p, k_p, k_m, k_p1, k_m1;
+// float dxx, dyy, dzz, dzz2, denom_xx, denom_yy, denom_zz, denom_zz2;
+// #pragma omp parallel for shared(U,D1,D2,D3,D4) private(i, j, k, i_p, i_m, j_m, j_p, k_p, k_m, denom_xx, denom_yy, denom_zz, denom_zz2, dxx, dyy, dzz, dzz2, k_p1, k_m1)
+// for(i=0; i<dimX; i++) {
+// /* symmetric boundary conditions (Neuman) */
+// i_p = i + 1; if (i_p == dimX) i_p = i - 1;
+// i_m = i - 1; if (i_m < 0) i_m = i + 1;
+// for(j=0; j<dimY; j++) {
+// j_p = j + 1; if (j_p == dimY) j_p = j - 1;
+// j_m = j - 1; if (j_m < 0) j_m = j + 1;
+// for(k=0; k<dimZ; k++) {
+// k_p = k + 1; if (k_p == dimZ) k_p = k - 1;
+// k_m = k - 1; if (k_m < 0) k_m = k + 1;
+// k_p1 = k + 2; if (k_p1 >= dimZ) k_p1 = k - 2;
+// k_m1 = k - 2; if (k_m1 < 0) k_m1 = k + 2;
+//
+// dxx = U[dimX*dimY*k + i_p*dimY + j] - 2.0f*U[dimX*dimY*k + i*dimY + j] + U[dimX*dimY*k + i_m*dimY + j];
+// dyy = U[dimX*dimY*k + i*dimY + j_p] - 2.0f*U[dimX*dimY*k + i*dimY + j] + U[dimX*dimY*k + i*dimY + j_m];
+// dzz = U[dimX*dimY*k_p + i*dimY + j] - 2.0f*U[dimX*dimY*k + i*dimY + j] + U[dimX*dimY*k_m + i*dimY + j];
+// dzz2 = U[dimX*dimY*k_p1 + i*dimY + j] - 2.0f*U[dimX*dimY*k + i*dimY + j] + U[dimX*dimY*k_m1 + i*dimY + j];
+//
+// denom_xx = fabs(dxx) + EPS;
+// denom_yy = fabs(dyy) + EPS;
+// denom_zz = fabs(dzz) + EPS;
+// denom_zz2 = fabs(dzz2) + EPS;
+//
+// D1[dimX*dimY*k + i*dimY + j] = dxx/denom_xx;
+// D2[dimX*dimY*k + i*dimY + j] = dyy/denom_yy;
+// D3[dimX*dimY*k + i*dimY + j] = dzz/denom_zz;
+// D4[dimX*dimY*k + i*dimY + j] = dzz2/denom_zz2;
+// }}}
+// return 1;
+// }
+
+float calcMap(float *U, unsigned short *Map, int dimX, int dimY, int dimZ)
+{
+ int i,j,k,i1,j1,i2,j2,windowSize;
+ float val1, val2,thresh_val,maxval;
+ windowSize = 1;
+ thresh_val = 0.0001; /*thresh_val = 0.0035;*/
+
+ /* normalize volume first */
+ maxval = 0.0f;
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ for(k=0; k<dimZ; k++) {
+ if (U[dimX*dimY*k + i*dimY + j] > maxval) maxval = U[dimX*dimY*k + i*dimY + j];
+ }}}
+
+ if (maxval != 0.0f) {
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ for(k=0; k<dimZ; k++) {
+ U[dimX*dimY*k + i*dimY + j] = U[dimX*dimY*k + i*dimY + j]/maxval;
+ }}}
+ }
+ else {
+ printf("%s \n", "Maximum value is zero!");
+ return 0;
+ }
+
+ #pragma omp parallel for shared(U,Map) private(i, j, k, i1, j1, i2, j2, val1, val2)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ for(k=0; k<dimZ; k++) {
+
+ Map[dimX*dimY*k + i*dimY + j] = 0;
+// Map2[dimX*dimY*k + i*dimY + j] = 0;
+
+ val1 = 0.0f; val2 = 0.0f;
+ for(i1=-windowSize; i1<=windowSize; i1++) {
+ for(j1=-windowSize; j1<=windowSize; j1++) {
+ i2 = i+i1;
+ j2 = j+j1;
+
+ if ((i2 >= 0) && (i2 < dimX) && (j2 >= 0) && (j2 < dimY)) {
+ if (k == 0) {
+ val1 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k+1) + i2*dimY + j2],2);
+// val3 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k+2) + i2*dimY + j2],2);
+ }
+ else if (k == dimZ-1) {
+ val1 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k-1) + i2*dimY + j2],2);
+// val3 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k-2) + i2*dimY + j2],2);
+ }
+// else if (k == 1) {
+// val1 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k-1) + i2*dimY + j2],2);
+// val2 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k+1) + i2*dimY + j2],2);
+// val3 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k+2) + i2*dimY + j2],2);
+// }
+// else if (k == dimZ-2) {
+// val1 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k-1) + i2*dimY + j2],2);
+// val2 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k+1) + i2*dimY + j2],2);
+// val3 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k-2) + i2*dimY + j2],2);
+// }
+ else {
+ val1 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k-1) + i2*dimY + j2],2);
+ val2 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k+1) + i2*dimY + j2],2);
+// val3 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k-2) + i2*dimY + j2],2);
+// val4 += pow(U[dimX*dimY*k + i2*dimY + j2] - U[dimX*dimY*(k+2) + i2*dimY + j2],2);
+ }
+ }
+ }}
+
+ val1 = 0.111f*val1; val2 = 0.111f*val2;
+// val3 = 0.111f*val3; val4 = 0.111f*val4;
+ if ((val1 <= thresh_val) && (val2 <= thresh_val)) Map[dimX*dimY*k + i*dimY + j] = 1;
+// if ((val3 <= thresh_val) && (val4 <= thresh_val)) Map2[dimX*dimY*k + i*dimY + j] = 1;
+ }}}
+ return 1;
+}
+
+float cleanMap(unsigned short *Map, int dimX, int dimY, int dimZ)
+{
+ int i, j, k, i1, j1, i2, j2, counter;
+ #pragma omp parallel for shared(Map) private(i, j, k, i1, j1, i2, j2, counter)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ for(k=0; k<dimZ; k++) {
+
+ counter=0;
+ for(i1=-3; i1<=3; i1++) {
+ for(j1=-3; j1<=3; j1++) {
+ i2 = i+i1;
+ j2 = j+j1;
+ if ((i2 >= 0) && (i2 < dimX) && (j2 >= 0) && (j2 < dimY)) {
+ if (Map[dimX*dimY*k + i2*dimY + j2] == 0) counter++;
+ }
+ }}
+ if (counter < 24) Map[dimX*dimY*k + i*dimY + j] = 1;
+ }}}
+ return *Map;
+}
+
+ /* Copy Image */
+ float copyIm(float *A, float *U, int dimX, int dimY, int dimZ)
+ {
+ int j;
+#pragma omp parallel for shared(A, U) private(j)
+ for(j=0; j<dimX*dimY*dimZ; j++) U[j] = A[j];
+ return *U;
+ }
+ /*********************3D *********************/ \ No newline at end of file
diff --git a/main_func/SplitBregman_TV.c b/main_func/SplitBregman_TV.c
new file mode 100644
index 0000000..691ccce
--- /dev/null
+++ b/main_func/SplitBregman_TV.c
@@ -0,0 +1,346 @@
+#include "mex.h"
+#include <matrix.h>
+#include <math.h>
+#include <stdlib.h>
+#include <memory.h>
+#include <stdio.h>
+#include "omp.h"
+
+/* C-OMP implementation of Split Bregman - TV denoising-regularization model (2D/3D)
+ *
+ * Input Parameters:
+ * 1. Noisy image/volume
+ * 2. lambda - regularization parameter
+ * 3. Number of iterations
+ * 4. eplsilon - tolerance constant
+ *
+ * Output:
+ * Filtered/regularized image
+ *
+ * Example:
+ * figure;
+ * Im = double(imread('lena_gray_256.tif'))/255; % loading image
+ * u0 = Im + .05*randn(size(Im)); u0(u0 < 0) = 0;
+ * u = SplitBregman_TV(single(u0), 10, 30, 1e-04);
+ *
+ * to compile with OMP support: mex SplitBregman_TV.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp"
+ * References:
+ * The Split Bregman Method for L1 Regularized Problems, by Tom Goldstein and Stanley Osher.
+ * D. Kazantsev, 2016*
+ */
+
+float copyIm(float *A, float *B, int dimX, int dimY, int dimZ);
+float gauss_seidel2D(float *U, float *A, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda, float mu);
+float updDxDy_shrink2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda);
+float updDxDy_shrinkAniso2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda);
+float updBxBy2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY);
+
+float gauss_seidel3D(float *U, float *A, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ, float lambda, float mu);
+float updDxDyDz_shrink3D(float *U, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ, float lambda);
+float updBxByBz3D(float *U, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ);
+
+void mexFunction(
+ int nlhs, mxArray *plhs[],
+ int nrhs, const mxArray *prhs[])
+
+{
+ int number_of_dims, iter, dimX, dimY, dimZ, ll, j, count;
+ const int *dim_array;
+ float *A, *U=NULL, *U_old=NULL, *Dx=NULL, *Dy=NULL, *Dz=NULL, *Bx=NULL, *By=NULL, *Bz=NULL, lambda, mu, epsil, re, re1, re_old;
+
+ number_of_dims = mxGetNumberOfDimensions(prhs[0]);
+ dim_array = mxGetDimensions(prhs[0]);
+
+ if(nrhs != 4) mexErrMsgTxt("Four input parameters is reqired: Image(2D/3D), Regularization parameter, Iterations, Tolerance");
+
+ /*Handling Matlab input data*/
+ A = (float *) mxGetData(prhs[0]); /*noisy image (2D/3D) */
+ mu = (float) mxGetScalar(prhs[1]); /* regularization parameter */
+ iter = (int) mxGetScalar(prhs[2]); /* iterations number */
+ epsil = (float) mxGetScalar(prhs[3]); /* tolerance constant */
+
+ lambda = 2.0f*2.0f;
+ count = 1;
+ re_old = 0.0f;
+ /*Handling Matlab output data*/
+ dimY = dim_array[0]; dimX = dim_array[1]; dimZ = dim_array[2];
+
+
+ if (number_of_dims == 2) {
+ dimZ = 1; /*2D case*/
+ U = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ U_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ Dx = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ Dy = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ Bx = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ By = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+
+ copyIm(A, U, dimX, dimY, dimZ); /*initialize */
+
+ /* begin outer SB iterations */
+ for(ll=0; ll<iter; ll++) {
+
+ /*storing old values*/
+ copyIm(U, U_old, dimX, dimY, dimZ);
+
+ gauss_seidel2D(U, A, Dx, Dy, Bx, By, dimX, dimY, lambda, mu);
+
+ updDxDy_shrink2D(U, Dx, Dy, Bx, By, dimX, dimY, lambda);
+ //updDxDy_shrinkAniso2D(U, Dx, Dy, Bx, By, dimX, dimY, lambda);
+
+ updBxBy2D(U, Dx, Dy, Bx, By, dimX, dimY);
+
+ /* calculate norm to terminate earlier */
+ re = 0.0f; re1 = 0.0f;
+ for(j=0; j<dimX*dimY*dimZ; j++)
+ {
+ re += pow(U_old[j] - U[j],2);
+ re1 += pow(U_old[j],2);
+ }
+ re = sqrt(re)/sqrt(re1);
+ if (re < epsil) count++;
+ if (count > 4) break;
+
+ /* check that the residual norm is decreasing */
+ if (ll > 2) {
+ if (re > re_old) break;
+ }
+ re_old = re;
+ /*printf("%f %i %i \n", re, ll, count); */
+
+ /*copyIm(U_old, U, dimX, dimY, dimZ); */
+ }
+ printf("SB iterations stopped at iteration: %i\n", ll);
+ }
+ if (number_of_dims == 3) {
+ U = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ U_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ Dx = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ Dy = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ Dz = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ Bx = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ By = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ Bz = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+
+ copyIm(A, U, dimX, dimY, dimZ); /*initialize */
+
+ /* begin outer SB iterations */
+ for(ll=0; ll<iter; ll++) {
+
+ /*storing old values*/
+ copyIm(U, U_old, dimX, dimY, dimZ);
+
+ gauss_seidel3D(U, A, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ, lambda, mu);
+
+ updDxDyDz_shrink3D(U, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ, lambda);
+
+ updBxByBz3D(U, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ);
+
+ /* calculate norm to terminate earlier */
+ re = 0.0f; re1 = 0.0f;
+ for(j=0; j<dimX*dimY*dimZ; j++)
+ {
+ re += pow(U[j] - U_old[j],2);
+ re1 += pow(U[j],2);
+ }
+ re = sqrt(re)/sqrt(re1);
+ if (re < epsil) count++;
+ if (count > 4) break;
+
+ /* check that the residual norm is decreasing */
+ if (ll > 2) {
+ if (re > re_old) break; }
+ /*printf("%f %i %i \n", re, ll, count); */
+ re_old = re;
+ }
+ printf("SB iterations stopped at iteration: %i\n", ll);
+ }
+}
+
+/* 2D-case related Functions */
+/*****************************************************************/
+float gauss_seidel2D(float *U, float *A, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda, float mu)
+{
+ float sum, normConst;
+ int i,j,i1,i2,j1,j2;
+ normConst = 1.0f/(mu + 4.0f*lambda);
+
+#pragma omp parallel for shared(U) private(i,j,i1,i2,j1,j2,sum)
+ for(i=0; i<dimX; i++) {
+ /* symmetric boundary conditions (Neuman) */
+ i1 = i+1; if (i1 == dimX) i1 = i-1;
+ i2 = i-1; if (i2 < 0) i2 = i+1;
+ for(j=0; j<dimY; j++) {
+ /* symmetric boundary conditions (Neuman) */
+ j1 = j+1; if (j1 == dimY) j1 = j-1;
+ j2 = j-1; if (j2 < 0) j2 = j+1;
+
+ sum = Dx[(i2)*dimY + (j)] - Dx[(i)*dimY + (j)] + Dy[(i)*dimY + (j2)] - Dy[(i)*dimY + (j)] - Bx[(i2)*dimY + (j)] + Bx[(i)*dimY + (j)] - By[(i)*dimY + (j2)] + By[(i)*dimY + (j)];
+ sum += (U[(i1)*dimY + (j)] + U[(i2)*dimY + (j)] + U[(i)*dimY + (j1)] + U[(i)*dimY + (j2)]);
+ sum *= lambda;
+ sum += mu*A[(i)*dimY + (j)];
+ U[(i)*dimY + (j)] = normConst*sum;
+ }}
+ return *U;
+}
+
+float updDxDy_shrink2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda)
+{
+ int i,j,i1,j1;
+ float val1, val11, val2, val22;
+
+ #pragma omp parallel for shared(U) private(i,j,i1,j1,val1,val11,val2,val22)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ /* symmetric boundary conditions (Neuman) */
+ i1 = i+1; if (i1 == dimX) i1 = i-1;
+ j1 = j+1; if (j1 == dimY) j1 = j-1;
+
+ val1 = (U[(i1)*dimY + (j)] - U[(i)*dimY + (j)]) + Bx[(i)*dimY + (j)];
+ val2 = (U[(i)*dimY + (j1)] - U[(i)*dimY + (j)]) + By[(i)*dimY + (j)];
+
+ val11 = fabs(val1) - 1.0f/lambda; if (val11 < 0) val11 = 0;
+ val22 = fabs(val2) - 1.0f/lambda; if (val22 < 0) val22 = 0;
+
+ if (val1 !=0) Dx[(i)*dimY + (j)] = (val1/fabs(val1))*val11; else Dx[(i)*dimY + (j)] = 0;
+ if (val2 !=0) Dy[(i)*dimY + (j)] = (val2/fabs(val2))*val22; else Dy[(i)*dimY + (j)] = 0;
+
+ }}
+ return 1;
+}
+float updDxDy_shrinkAniso2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda)
+{
+ int i,j,i1,j1;
+ float val1, val11, val2, denom, denom_lam;
+ denom_lam = 1.0f/lambda;
+
+ #pragma omp parallel for shared(U) private(i,j,i1,j1,val1,val11,val2,denom,denom_lam)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ /* symmetric boundary conditions (Neuman) */
+ i1 = i+1; if (i1 == dimX) i1 = i-1;
+ j1 = j+1; if (j1 == dimY) j1 = j-1;
+
+ val1 = (U[(i1)*dimY + (j)] - U[(i)*dimY + (j)]) + Bx[(i)*dimY + (j)];
+ val2 = (U[(i)*dimY + (j1)] - U[(i)*dimY + (j)]) + By[(i)*dimY + (j)];
+
+ denom = sqrt(val1*val1 + val2*val2);
+
+ val11 = (denom - denom_lam); if (val11 < 0) val11 = 0.0f;
+
+ if (denom != 0.0f) {
+ Dx[(i)*dimY + (j)] = val11*(val1/denom);
+ Dy[(i)*dimY + (j)] = val11*(val2/denom);
+ }
+ else {
+ Dx[(i)*dimY + (j)] = 0;
+ Dy[(i)*dimY + (j)] = 0;
+ }
+ }}
+ return 1;
+}
+float updBxBy2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY)
+{
+ int i,j,i1,j1;
+ #pragma omp parallel for shared(U) private(i,j,i1,j1)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ /* symmetric boundary conditions (Neuman) */
+ i1 = i+1; if (i1 == dimX) i1 = i-1;
+ j1 = j+1; if (j1 == dimY) j1 = j-1;
+
+ Bx[(i)*dimY + (j)] = Bx[(i)*dimY + (j)] + ((U[(i1)*dimY + (j)] - U[(i)*dimY + (j)]) - Dx[(i)*dimY + (j)]);
+ By[(i)*dimY + (j)] = By[(i)*dimY + (j)] + ((U[(i)*dimY + (j1)] - U[(i)*dimY + (j)]) - Dy[(i)*dimY + (j)]);
+ }}
+ return 1;
+}
+
+
+/* 3D-case related Functions */
+/*****************************************************************/
+float gauss_seidel3D(float *U, float *A, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ, float lambda, float mu)
+{
+ float normConst, d_val, b_val, sum;
+ int i,j,i1,i2,j1,j2,k,k1,k2;
+ normConst = 1.0f/(mu + 6.0f*lambda);
+#pragma omp parallel for shared(U) private(i,j,i1,i2,j1,j2,k,k1,k2,d_val,b_val,sum)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ for(k=0; k<dimZ; k++) {
+ /* symmetric boundary conditions (Neuman) */
+ i1 = i+1; if (i1 == dimX) i1 = i-1;
+ i2 = i-1; if (i2 < 0) i2 = i+1;
+ j1 = j+1; if (j1 == dimY) j1 = j-1;
+ j2 = j-1; if (j2 < 0) j2 = j+1;
+ k1 = k+1; if (k1 == dimZ) k1 = k-1;
+ k2 = k-1; if (k2 < 0) k2 = k+1;
+
+ d_val = Dx[(dimX*dimY)*k + (i2)*dimY + (j)] - Dx[(dimX*dimY)*k + (i)*dimY + (j)] + Dy[(dimX*dimY)*k + (i)*dimY + (j2)] - Dy[(dimX*dimY)*k + (i)*dimY + (j)] + Dz[(dimX*dimY)*k2 + (i)*dimY + (j)] - Dz[(dimX*dimY)*k + (i)*dimY + (j)];
+ b_val = -Bx[(dimX*dimY)*k + (i2)*dimY + (j)] + Bx[(dimX*dimY)*k + (i)*dimY + (j)] - By[(dimX*dimY)*k + (i)*dimY + (j2)] + By[(dimX*dimY)*k + (i)*dimY + (j)] - Bz[(dimX*dimY)*k2 + (i)*dimY + (j)] + Bz[(dimX*dimY)*k + (i)*dimY + (j)];
+ sum = d_val + b_val;
+ sum += U[(dimX*dimY)*k + (i1)*dimY + (j)] + U[(dimX*dimY)*k + (i2)*dimY + (j)] + U[(dimX*dimY)*k + (i)*dimY + (j1)] + U[(dimX*dimY)*k + (i)*dimY + (j2)] + U[(dimX*dimY)*k1 + (i)*dimY + (j)] + U[(dimX*dimY)*k2 + (i)*dimY + (j)];
+ sum *= lambda;
+ sum += mu*A[(dimX*dimY)*k + (i)*dimY + (j)];
+ U[(dimX*dimY)*k + (i)*dimY + (j)] = normConst*sum;
+ }}}
+ return *U;
+}
+
+float updDxDyDz_shrink3D(float *U, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ, float lambda)
+{
+ int i,j,i1,j1,k,k1;
+ float val1, val11, val2, val22, val3, val33;
+
+ #pragma omp parallel for shared(U) private(i,j,i1,j1,k,k1,val1,val11,val2,val22,val3,val33)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ for(k=0; k<dimZ; k++) {
+ /* symmetric boundary conditions (Neuman) */
+ i1 = i+1; if (i1 == dimX) i1 = i-1;
+ j1 = j+1; if (j1 == dimY) j1 = j-1;
+ k1 = k+1; if (k1 == dimZ) k1 = k-1;
+
+ val1 = (U[(dimX*dimY)*k + (i1)*dimY + (j)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) + Bx[(dimX*dimY)*k + (i)*dimY + (j)];
+ val2 = (U[(dimX*dimY)*k + (i)*dimY + (j1)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) + By[(dimX*dimY)*k + (i)*dimY + (j)];
+ val3 = (U[(dimX*dimY)*k1 + (i)*dimY + (j)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) + Bz[(dimX*dimY)*k + (i)*dimY + (j)];
+
+ val11 = fabs(val1) - 1.0f/lambda; if (val11 < 0) val11 = 0;
+ val22 = fabs(val2) - 1.0f/lambda; if (val22 < 0) val22 = 0;
+ val33 = fabs(val3) - 1.0f/lambda; if (val33 < 0) val33 = 0;
+
+ if (val1 !=0) Dx[(dimX*dimY)*k + (i)*dimY + (j)] = (val1/fabs(val1))*val11; else Dx[(dimX*dimY)*k + (i)*dimY + (j)] = 0;
+ if (val2 !=0) Dy[(dimX*dimY)*k + (i)*dimY + (j)] = (val2/fabs(val2))*val22; else Dy[(dimX*dimY)*k + (i)*dimY + (j)] = 0;
+ if (val3 !=0) Dz[(dimX*dimY)*k + (i)*dimY + (j)] = (val3/fabs(val3))*val33; else Dz[(dimX*dimY)*k + (i)*dimY + (j)] = 0;
+
+ }}}
+ return 1;
+}
+float updBxByBz3D(float *U, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ)
+{
+ int i,j,k,i1,j1,k1;
+ #pragma omp parallel for shared(U) private(i,j,k,i1,j1,k1)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ for(k=0; k<dimZ; k++) {
+ /* symmetric boundary conditions (Neuman) */
+ i1 = i+1; if (i1 == dimX) i1 = i-1;
+ j1 = j+1; if (j1 == dimY) j1 = j-1;
+ k1 = k+1; if (k1 == dimZ) k1 = k-1;
+
+ Bx[(dimX*dimY)*k + (i)*dimY + (j)] = Bx[(dimX*dimY)*k + (i)*dimY + (j)] + ((U[(dimX*dimY)*k + (i1)*dimY + (j)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) - Dx[(dimX*dimY)*k + (i)*dimY + (j)]);
+ By[(dimX*dimY)*k + (i)*dimY + (j)] = By[(dimX*dimY)*k + (i)*dimY + (j)] + ((U[(dimX*dimY)*k + (i)*dimY + (j1)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) - Dy[(dimX*dimY)*k + (i)*dimY + (j)]);
+ Bz[(dimX*dimY)*k + (i)*dimY + (j)] = Bz[(dimX*dimY)*k + (i)*dimY + (j)] + ((U[(dimX*dimY)*k1 + (i)*dimY + (j)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) - Dz[(dimX*dimY)*k + (i)*dimY + (j)]);
+
+ }}}
+ return 1;
+}
+/* General Functions */
+/*****************************************************************/
+/* Copy Image */
+float copyIm(float *A, float *B, int dimX, int dimY, int dimZ)
+{
+ int j;
+#pragma omp parallel for shared(A, B) private(j)
+ for(j=0; j<dimX*dimY*dimZ; j++) B[j] = A[j];
+ return *B;
+} \ No newline at end of file
diff --git a/main_func/compile_mex.m b/main_func/compile_mex.m
new file mode 100644
index 0000000..ea6e3a5
--- /dev/null
+++ b/main_func/compile_mex.m
@@ -0,0 +1,4 @@
+% compile mex's
+mex LLT_model.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp"
+mex FISTA_TV.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp"
+mex SplitBregman_TV.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp" \ No newline at end of file
diff --git a/main_func/studentst.m b/main_func/studentst.m
new file mode 100644
index 0000000..99fed1e
--- /dev/null
+++ b/main_func/studentst.m
@@ -0,0 +1,47 @@
+function [f,g,h,s,k] = studentst(r,k,s)
+% Students T penalty with 'auto-tuning'
+%
+% use:
+% [f,g,h,{k,{s}}] = studentst(r) - automatically fits s and k
+% [f,g,h,{k,{s}}] = studentst(r,k) - automatically fits s
+% [f,g,h,{k,{s}}] = studentst(r,k,s) - use given s and k
+%
+% input:
+% r - residual as column vector
+% s - scale (optional)
+% k - degrees of freedom (optional)
+%
+% output:
+% f - misfit (scalar)
+% g - gradient (column vector)
+% h - positive approximation of the Hessian (column vector, Hessian is a diagonal matrix)
+% s,k - scale and degrees of freedom
+%
+% Tristan van Leeuwen, 2012.
+% tleeuwen@eos.ubc.ca
+
+% fit both s and k
+if nargin == 1
+ opts = optimset('maxFunEvals',1e2);
+ tmp = fminsearch(@(x)st(r,x(1),x(2)),[1;2],opts);
+ s = tmp(1);
+ k = tmp(2);
+end
+
+
+if nargin == 2
+ opts = optimset('maxFunEvals',1e2);
+ tmp = fminsearch(@(x)st(r,x,k),[1],opts);
+ s = tmp(1);
+end
+
+% evaulate penalty
+[f,g,h] = st(r,s,k);
+
+
+function [f,g,h] = st(r,s,k)
+n = length(r);
+c = -n*(gammaln((k+1)/2) - gammaln(k/2) - .5*log(pi*s*k));
+f = c + .5*(k+1)*sum(log(1 + conj(r).*r/(s*k)));
+g = (k+1)*r./(s*k + conj(r).*r);
+h = (k+1)./(s*k + conj(r).*r);
diff --git a/readme.doc b/readme.doc
new file mode 100644
index 0000000..705cd01
--- /dev/null
+++ b/readme.doc
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diff --git a/readme.pdf b/readme.pdf
new file mode 100644
index 0000000..56f3ff7
--- /dev/null
+++ b/readme.pdf
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diff --git a/supp/RMSE.m b/supp/RMSE.m
new file mode 100644
index 0000000..734e4b8
--- /dev/null
+++ b/supp/RMSE.m
@@ -0,0 +1,7 @@
+function err = RMSE(signal1, signal2)
+%RMSE Root Mean Squared Error
+
+err = sum((signal1 - signal2).^2)/length(signal1); % MSE
+err = sqrt(err); % RMSE
+
+end \ No newline at end of file
diff --git a/supp/add_wedges.m b/supp/add_wedges.m
new file mode 100644
index 0000000..8b8f2a7
--- /dev/null
+++ b/supp/add_wedges.m
@@ -0,0 +1,30 @@
+% create a wedge mask to simulate the missing wedge
+
+[rows, columns] = size(sino_zing_rings);
+grayImage = ones(rows, columns, 'uint8');
+xCoords = [0 360 0];
+yCoords = [35 7 7];
+mask = poly2mask(xCoords, yCoords, rows, columns);
+grayImage(mask) = 0;
+
+xCoords = [727 360 727];
+yCoords = [35 7 7];
+mask = poly2mask(xCoords, yCoords, rows, columns);
+grayImage(mask) = 0;
+
+xCoords = [0 360 0];
+yCoords = [145 173 173];
+mask = poly2mask(xCoords, yCoords, rows, columns);
+grayImage(mask) = 0;
+
+xCoords = [727 360 727];
+yCoords = [145 173 173];
+mask = poly2mask(xCoords, yCoords, rows, columns);
+grayImage(mask) = 0;
+
+grayImage(1:7,:) = 0;
+grayImage(173:end,:) = 0;
+
+%figure; imshow(grayImage, [0 1]);
+MW_sino_artifacts = sino_zing_rings.*double(grayImage);
+%Dweights = Dweights.*double(grayImage); \ No newline at end of file
diff --git a/supp/filtersinc.m b/supp/filtersinc.m
new file mode 100644
index 0000000..6c29c98
--- /dev/null
+++ b/supp/filtersinc.m
@@ -0,0 +1,28 @@
+function g = filtersinc(PR)
+
+
+% filtersinc.m
+%
+% Written by Waqas Akram
+%
+% "a": This parameter varies the filter magnitude response.
+% When "a" is very small (a<<1), the response approximates |w|
+% As "a" is increased, the filter response starts to
+% roll off at high frequencies.
+a = 1;
+
+[Length, Count] = size(PR);
+w = [-pi:(2*pi)/Length:pi-(2*pi)/Length];
+
+rn1 = abs(2/a*sin(a.*w./2));
+rn2 = sin(a.*w./2);
+rd = (a*w)./2;
+r = rn1*(rn2/rd)^2;
+
+f = fftshift(r);
+for i = 1:Count
+ IMG = fft(PR(:,i));
+ fimg = IMG.*f';
+ g(:,i) = ifft(fimg);
+end
+g = real(g); \ No newline at end of file
diff --git a/supp/my_red_yellowMAP.mat b/supp/my_red_yellowMAP.mat
new file mode 100644
index 0000000..c2a5b87
--- /dev/null
+++ b/supp/my_red_yellowMAP.mat
Binary files differ
diff --git a/supp/ssim_index.m b/supp/ssim_index.m
new file mode 100644
index 0000000..4fa7a79
--- /dev/null
+++ b/supp/ssim_index.m
@@ -0,0 +1,181 @@
+function [mssim, ssim_map] = ssim_index(img1, img2, K, window, L)
+
+%========================================================================
+%SSIM Index, Version 1.0
+%Copyright(c) 2003 Zhou Wang
+%All Rights Reserved.
+%
+%This is an implementation of the algorithm for calculating the
+%Structural SIMilarity (SSIM) index between two images. Please refer
+%to the following paper:
+%
+%Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image
+%quality assessment: From error visibility to structural similarity"
+%IEEE Transactios on Image Processing, vol. 13, no. 4, pp.600-612,
+%Apr. 2004.
+%
+%Kindly report any suggestions or corrections to zhouwang@ieee.org
+%
+%----------------------------------------------------------------------
+%
+%Input : (1) img1: the first image being compared
+% (2) img2: the second image being compared
+% (3) K: constants in the SSIM index formula (see the above
+% reference). defualt value: K = [0.01 0.03]
+% (4) window: local window for statistics (see the above
+% reference). default widnow is Gaussian given by
+% window = fspecial('gaussian', 11, 1.5);
+% (5) L: dynamic range of the images. default: L = 255
+%
+%Output: (1) mssim: the mean SSIM index value between 2 images.
+% If one of the images being compared is regarded as
+% perfect quality, then mssim can be considered as the
+% quality measure of the other image.
+% If img1 = img2, then mssim = 1.
+% (2) ssim_map: the SSIM index map of the test image. The map
+% has a smaller size than the input images. The actual size:
+% size(img1) - size(window) + 1.
+%
+%Default Usage:
+% Given 2 test images img1 and img2, whose dynamic range is 0-255
+%
+% [mssim ssim_map] = ssim_index(img1, img2);
+%
+%Advanced Usage:
+% User defined parameters. For example
+%
+% K = [0.05 0.05];
+% window = ones(8);
+% L = 100;
+% [mssim ssim_map] = ssim_index(img1, img2, K, window, L);
+%
+%See the results:
+%
+% mssim %Gives the mssim value
+% imshow(max(0, ssim_map).^4) %Shows the SSIM index map
+%
+%========================================================================
+
+
+if (nargin < 2 | nargin > 5)
+ ssim_index = -Inf;
+ ssim_map = -Inf;
+ return;
+end
+
+if (size(img1) ~= size(img2))
+ ssim_index = -Inf;
+ ssim_map = -Inf;
+ return;
+end
+
+[M N] = size(img1);
+
+if (nargin == 2)
+ if ((M < 11) | (N < 11)) % ͼССû塣
+ ssim_index = -Inf;
+ ssim_map = -Inf;
+ return
+ end
+ window = fspecial('gaussian', 11, 1.5); % һ׼ƫ1.511*11ĸ˹ͨ˲
+ K(1) = 0.01; % default settings
+ K(2) = 0.03; %
+ L = 255; %
+end
+
+if (nargin == 3)
+ if ((M < 11) | (N < 11))
+ ssim_index = -Inf;
+ ssim_map = -Inf;
+ return
+ end
+ window = fspecial('gaussian', 11, 1.5);
+ L = 255;
+ if (length(K) == 2)
+ if (K(1) < 0 | K(2) < 0)
+ ssim_index = -Inf;
+ ssim_map = -Inf;
+ return;
+ end
+ else
+ ssim_index = -Inf;
+ ssim_map = -Inf;
+ return;
+ end
+end
+
+if (nargin == 4)
+ [H W] = size(window);
+ if ((H*W) < 4 | (H > M) | (W > N))
+ ssim_index = -Inf;
+ ssim_map = -Inf;
+ return
+ end
+ L = 255;
+ if (length(K) == 2)
+ if (K(1) < 0 | K(2) < 0)
+ ssim_index = -Inf;
+ ssim_map = -Inf;
+ return;
+ end
+ else
+ ssim_index = -Inf;
+ ssim_map = -Inf;
+ return;
+ end
+end
+
+if (nargin == 5)
+ [H W] = size(window);
+ if ((H*W) < 4 | (H > M) | (W > N))
+ ssim_index = -Inf;
+ ssim_map = -Inf;
+ return
+ end
+ if (length(K) == 2)
+ if (K(1) < 0 | K(2) < 0)
+ ssim_index = -Inf;
+ ssim_map = -Inf;
+ return;
+ end
+ else
+ ssim_index = -Inf;
+ ssim_map = -Inf;
+ return;
+ end
+end
+%%
+C1 = (K(1)*L)^2; % C1Lxyá
+C2 = (K(2)*L)^2; % C2ԱȶCxyá
+window = window/sum(sum(window)); %˲һ
+img1 = double(img1);
+img2 = double(img2);
+
+mu1 = filter2(window, img1, 'valid'); % ͼ˲ӼȨ
+mu2 = filter2(window, img2, 'valid'); % ͼ˲ӼȨ
+
+mu1_sq = mu1.*mu1; % Uxƽֵ
+mu2_sq = mu2.*mu2; % Uyƽֵ
+mu1_mu2 = mu1.*mu2; % Ux*Uyֵ
+
+sigma1_sq = filter2(window, img1.*img1, 'valid') - mu1_sq; % sigmax ׼
+sigma2_sq = filter2(window, img2.*img2, 'valid') - mu2_sq; % sigmay ׼
+sigma12 = filter2(window, img1.*img2, 'valid') - mu1_mu2; % sigmaxy׼
+
+if (C1 > 0 & C2 > 0)
+ ssim_map = ((2*mu1_mu2 + C1).*(2*sigma12 + C2))./((mu1_sq + mu2_sq + C1).*(sigma1_sq + sigma2_sq + C2));
+else
+ numerator1 = 2*mu1_mu2 + C1;
+ numerator2 = 2*sigma12 + C2;
+ denominator1 = mu1_sq + mu2_sq + C1;
+ denominator2 = sigma1_sq + sigma2_sq + C2;
+ ssim_map = ones(size(mu1));
+ index = (denominator1.*denominator2 > 0);
+ ssim_map(index) = (numerator1(index).*numerator2(index))./(denominator1(index).*denominator2(index));
+ index = (denominator1 ~= 0) & (denominator2 == 0);
+ ssim_map(index) = numerator1(index)./denominator1(index);
+end
+
+mssim = mean2(ssim_map);
+
+return \ No newline at end of file
diff --git a/supp/subplot_tight.m b/supp/subplot_tight.m
new file mode 100644
index 0000000..0b0cbd5
--- /dev/null
+++ b/supp/subplot_tight.m
@@ -0,0 +1 @@
+function vargout=subplot_tight(m, n, p, margins, varargin) %% subplot_tight % A subplot function substitude with margins user tunabble parameter. % %% Syntax % h=subplot_tight(m, n, p); % h=subplot_tight(m, n, p, margins); % h=subplot_tight(m, n, p, margins, subplotArgs...); % %% Description % Our goal is to grant the user the ability to define the margins between neighbouring % subplots. Unfotrtunately Matlab subplot function lacks this functionality, and the % margins between subplots can reach 40% of figure area, which is pretty lavish. While at % the begining the function was implememnted as wrapper function for Matlab function % subplot, it was modified due to axes del;etion resulting from what Matlab subplot % detected as overlapping. Therefore, the current implmenetation makes no use of Matlab % subplot function, using axes instead. This can be problematic, as axis and subplot % parameters are quie different. Set isWrapper to "True" to return to wrapper mode, which % fully supports subplot format. % %% Input arguments (defaults exist): % margins- two elements vector [vertical,horizontal] defining the margins between % neighbouring axes. Default value is 0.04 % %% Output arguments % same as subplot- none, or axes handle according to function call. % %% Issues & Comments % - Note that if additional elements are used in order to be passed to subplot, margins % parameter must be defined. For default margins value use empty element- []. % - % %% Example % close all; % img=imread('peppers.png'); % figSubplotH=figure('Name', 'subplot'); % figSubplotTightH=figure('Name', 'subplot_tight'); % nElems=17; % subplotRows=ceil(sqrt(nElems)-1); % subplotRows=max(1, subplotRows); % subplotCols=ceil(nElems/subplotRows); % for iElem=1:nElems % figure(figSubplotH); % subplot(subplotRows, subplotCols, iElem); % imshow(img); % figure(figSubplotTightH); % subplot_tight(subplotRows, subplotCols, iElem, [0.0001]); % imshow(img); % end % %% See also % - subplot % %% Revision history % First version: Nikolay S. 2011-03-29. % Last update: Nikolay S. 2012-05-24. % % *List of Changes:* % 2012-05-24 % Non wrapping mode (based on axes command) added, to deal with an issue of disappearing % subplots occuring with massive axes. %% Default params isWrapper=false; if (nargin<4) || isempty(margins) margins=[0.04,0.04]; % default margins value- 4% of figure end if length(margins)==1 margins(2)=margins; end %note n and m are switched as Matlab indexing is column-wise, while subplot indexing is row-wise :( [subplot_col,subplot_row]=ind2sub([n,m],p); height=(1-(m+1)*margins(1))/m; % single subplot height width=(1-(n+1)*margins(2))/n; % single subplot width % note subplot suppors vector p inputs- so a merged subplot of higher dimentions will be created subplot_cols=1+max(subplot_col)-min(subplot_col); % number of column elements in merged subplot subplot_rows=1+max(subplot_row)-min(subplot_row); % number of row elements in merged subplot merged_height=subplot_rows*( height+margins(1) )- margins(1); % merged subplot height merged_width= subplot_cols*( width +margins(2) )- margins(2); % merged subplot width merged_bottom=(m-max(subplot_row))*(height+margins(1)) +margins(1); % merged subplot bottom position merged_left=min(subplot_col)*(width+margins(2))-width; % merged subplot left position pos=[merged_left, merged_bottom, merged_width, merged_height]; if isWrapper h=subplot(m, n, p, varargin{:}, 'Units', 'Normalized', 'Position', pos); else h=axes('Position', pos, varargin{:}); end if nargout==1 vargout=h; end \ No newline at end of file
diff --git a/supp/zing_rings_add.m b/supp/zing_rings_add.m
new file mode 100644
index 0000000..023ac27
--- /dev/null
+++ b/supp/zing_rings_add.m
@@ -0,0 +1,84 @@
+% uncomment this part of script to generate data with different noise characterisitcs
+
+fprintf('%s\n', 'Generating Projection Data...');
+multfactor = 1000;
+% Creating RHS (b) - the sinogram (using a strip projection model)
+vol_geom = astra_create_vol_geom(N, N);
+proj_geom = astra_create_proj_geom('parallel', 1.0, P, theta_rad);
+proj_id_temp = astra_create_projector('strip', proj_geom, vol_geom);
+[sinogram_id, sinogramIdeal] = astra_create_sino(phantom./multfactor, proj_id_temp);
+astra_mex_data2d('delete',sinogram_id);
+astra_mex_algorithm('delete',proj_id_temp);
+%
+% % adding Gaussian noise
+% eta = 0.04; % Relative noise level
+% E = randn(size(sinogram));
+% sinogram = sinogram + eta*norm(sinogram,'fro')*E/norm(E,'fro'); % adding noise to the sinogram
+% sinogram(sinogram<0) = 0;
+% clear E;
+
+%%
+% adding zingers
+val_offset = 0;
+sino_zing = sinogramIdeal;
+vec1 = [60, 80, 80, 70, 70, 90, 90, 40, 130, 145, 155, 125];
+vec2 = [350, 450, 190, 500, 250, 530, 330, 230, 550, 250, 450, 195];
+for jj = 1:length(vec1)
+ for i1 = -2:2
+ for j1 = -2:2
+ sino_zing(vec1(jj)+i1, vec2(jj)+j1) = val_offset;
+ end
+ end
+end
+
+% adding stripes into the signogram
+sino_zing_rings = sino_zing;
+coeff = linspace2(0.01,0.15,180);
+vmax = max(sinogramIdeal(:));
+sino_zing_rings(1:180,120) = sino_zing_rings(1:180,120) + vmax*0.13;
+sino_zing_rings(80:180,209) = sino_zing_rings(80:180,209) + vmax*0.14;
+sino_zing_rings(50:110,210) = sino_zing_rings(50:110,210) + vmax*0.12;
+sino_zing_rings(1:180,211) = sino_zing_rings(1:180,211) + vmax*0.14;
+sino_zing_rings(1:180,300) = sino_zing_rings(1:180,300) + vmax*coeff(:);
+sino_zing_rings(1:180,301) = sino_zing_rings(1:180,301) + vmax*0.14;
+sino_zing_rings(10:100,302) = sino_zing_rings(10:100,302) + vmax*0.15;
+sino_zing_rings(90:180,350) = sino_zing_rings(90:180,350) + vmax*0.11;
+sino_zing_rings(60:140,410) = sino_zing_rings(60:140,410) + vmax*0.12;
+sino_zing_rings(1:180,411) = sino_zing_rings(1:180,411) + vmax*0.14;
+sino_zing_rings(1:180,412) = sino_zing_rings(1:180,412) + vmax*coeff(:);
+sino_zing_rings(1:180,413) = sino_zing_rings(1:180,413) + vmax*coeff(:);
+sino_zing_rings(1:180,500) = sino_zing_rings(1:180,500) - vmax*0.12;
+sino_zing_rings(1:180,501) = sino_zing_rings(1:180,501) - vmax*0.12;
+sino_zing_rings(1:180,550) = sino_zing_rings(1:180,550) + vmax*0.11;
+sino_zing_rings(1:180,551) = sino_zing_rings(1:180,551) + vmax*0.11;
+sino_zing_rings(1:180,552) = sino_zing_rings(1:180,552) + vmax*0.11;
+
+sino_zing_rings(sino_zing_rings < 0) = 0;
+%%
+
+% adding Poisson noise
+dose = 50000;
+dataExp = dose.*exp(-sino_zing_rings); % noiseless raw data
+dataPnoise = astra_add_noise_to_sino(dataExp,2*dose); % pre-log noisy raw data (weights)
+Dweights = dataPnoise;
+sinogram = log(dose./dataPnoise); %log corrected data -> sinogram
+sinogram = abs(sinogram);
+clear dataPnoise dataExp
+
+% normalizing
+sinogram = sinogram.*multfactor;
+sino_zing_rings = sinogram;
+Dweights = multfactor./Dweights;
+
+%
+% figure(1);
+% set(gcf, 'Position', get(0,'Screensize'));
+% subplot(1,2,1); imshow(phantom,[0 0.6]); title('Ideal Phantom'); colorbar;
+% subplot(1,2,2); imshow(sinogram,[0 180]); title('Noisy Sinogram'); colorbar;
+% colormap(cmapnew);
+
+% figure;
+% set(gcf, 'Position', get(0,'Screensize'));
+% subplot(1,2,1); imshow(sinogramIdeal,[0 180]); title('Ideal Sinogram'); colorbar;
+% imshow(sino_zing_rings,[0 180]); title('Noisy Sinogram with zingers and stripes'); colorbar;
+% colormap(cmapnew); \ No newline at end of file
diff --git a/~$readme.doc b/~$readme.doc
new file mode 100644
index 0000000..3de8b72
--- /dev/null
+++ b/~$readme.doc
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