Initial revision

6 files changed, 1497 insertions, 0 deletions

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);