From 329a104d4cb5ba50a59fb80e58de0453ba49f075 Mon Sep 17 00:00:00 2001
From: Daniil Kazantsev <dkazanc@hotmail.com>
Date: Mon, 3 Jul 2017 22:35:23 +0100
Subject: Major reorganization, updated routines

---
 main_func/FGP_TV.c          | 400 ++++++++++++++++++++++++++++++++++++++++++++
 main_func/FISTA_REC.m       | 291 ++++++++++++++++----------------
 main_func/FISTA_TV.c        | 331 ------------------------------------
 main_func/LLT_model.c       |   2 +-
 main_func/SplitBregman_TV.c | 317 ++++++++++++++++++++---------------
 main_func/compile_mex.m     |   4 +-
 main_func/studentst.m       |  94 +++++------
 7 files changed, 785 insertions(+), 654 deletions(-)
 create mode 100644 main_func/FGP_TV.c
 delete mode 100644 main_func/FISTA_TV.c

(limited to 'main_func')

diff --git a/main_func/FGP_TV.c b/main_func/FGP_TV.c
new file mode 100644
index 0000000..1a1fd13
--- /dev/null
+++ b/main_func/FGP_TV.c
@@ -0,0 +1,400 @@
+#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 FGP-TV [1] denoising/regularization model (2D/3D case)
+ *
+ * Input Parameters:
+ * 1. Noisy image/volume [REQUIRED]
+ * 2. lambda - regularization parameter [REQUIRED]
+ * 3. Number of iterations [OPTIONAL parameter]
+ * 4. eplsilon: tolerance constant [OPTIONAL parameter]
+ * 5. TV-type: 'iso' or 'l1' [OPTIONAL parameter]
+ *
+ * Output:
+ * [1] Filtered/regularized image
+ * [2] last function value 
+ *
+ * Example of image denoising:
+ * figure;
+ * Im = double(imread('lena_gray_256.tif'))/255;  % loading image
+ * u0 = Im + .05*randn(size(Im)); % adding noise
+ * u = FGP_TV(single(u0), 0.05, 100, 1e-04);
+ *
+ * to compile with OMP support: mex FGP_TV.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp"
+ * This function is based on the Matlab's code and paper by
+ * [1] Amir Beck and Marc Teboulle, "Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems"
+ *
+ * D. Kazantsev, 2016-17
+ *
+ */
+
+float copyIm(float *A, float *B, int dimX, int dimY, int dimZ);
+float Obj_func2D(float *A, float *D, float *R1, float *R2, 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 methTV, 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, methTV;
+    const int  *dim_array;
+    float *A, *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, funcval;
+    
+    number_of_dims = mxGetNumberOfDimensions(prhs[0]);
+    dim_array = mxGetDimensions(prhs[0]);
+    
+    /*Handling Matlab input data*/
+    if ((nrhs < 2) || (nrhs > 5)) mexErrMsgTxt("At least 2 parameters is required: Image(2D/3D), Regularization parameter. The full list of parameters: Image(2D/3D), Regularization parameter, iterations number, tolerance, penalty type ('iso' or 'l1')");
+    
+    A  = (float *) mxGetData(prhs[0]); /*noisy image (2D/3D) */
+    lambda =  (float) mxGetScalar(prhs[1]); /* regularization parameter */
+    iter = 50; /* default iterations number */
+    epsil = 0.001; /* default tolerance constant */
+    methTV = 0;  /* default isotropic TV penalty */
+    
+    if ((nrhs == 3) || (nrhs == 4) || (nrhs == 5))  iter = (int) mxGetScalar(prhs[2]); /* iterations number */
+    if ((nrhs == 4) || (nrhs == 5))  epsil =  (float) mxGetScalar(prhs[3]); /* tolerance constant */
+    if (nrhs == 5)  {
+        char *penalty_type;
+        penalty_type = mxArrayToString(prhs[4]); /* choosing TV penalty: 'iso' or 'l1', 'iso' is the default */
+        if ((strcmp(penalty_type, "l1") != 0) && (strcmp(penalty_type, "iso") != 0)) mexErrMsgTxt("Choose TV type: 'iso' or 'l1',");
+        if (strcmp(penalty_type, "l1") == 0)  methTV = 1;  /* enable 'l1' penalty */
+        mxFree(penalty_type);
+    }
+    /*output function value (last iteration) */
+    funcval = 0.0f;
+    plhs[1] = mxCreateNumericMatrix(1, 1, mxSINGLE_CLASS, mxREAL);  
+    float *funcvalA = (float *) mxGetData(plhs[1]);
+        
+    if (mxGetClassID(prhs[0]) != mxSINGLE_CLASS) {mexErrMsgTxt("The input image must be in a single precision"); }
+    
+    /*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));
+        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++) {
+            
+            /* computing the gradient of the objective function */
+            Obj_func2D(A, D, R1, R2, 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, methTV, 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) {
+                Obj_func2D(A, D, P1, P2, lambda, dimX, dimY);            
+                funcval = 0.0f; 
+                for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2);                           
+                funcvalA[0] = sqrt(funcval);     
+                break; }
+            
+            /* check that the residual norm is decreasing */
+            if (ll > 2) {
+                if (re > re_old) {
+                    Obj_func2D(A, D, P1, P2, lambda, dimX, dimY);            
+                    funcval = 0.0f; 
+                    for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2);                           
+                    funcvalA[0] = sqrt(funcval);                     
+                    break; }}            
+            re_old = re;
+            /*printf("%f %i %i \n", re, ll, count); */
+            
+            /*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;
+            
+            /* calculating the objective function value */
+            if (ll == (iter-1)) {
+            Obj_func2D(A, D, P1, P2, lambda, dimX, dimY);            
+            funcval = 0.0f; 
+            for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2);                           
+            funcvalA[0] = sqrt(funcval);            
+            }
+        }
+        printf("FGP-TV iterations stopped at iteration %i with the function value %f \n", ll, funcvalA[0]);
+    }
+    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++) {
+            
+            /* 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) {
+                Obj_func3D(A, D, P1, P2, P3,lambda, dimX, dimY, dimZ);
+                funcval = 0.0f; 
+                for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2);                           
+                funcvalA[0] = sqrt(funcval);                  
+                break;}
+            
+            /* check that the residual norm is decreasing */
+            if (ll > 2) {
+                if (re > re_old) {
+                Obj_func3D(A, D, P1, P2, P3,lambda, dimX, dimY, dimZ);
+                funcval = 0.0f; 
+                for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2);                           
+                funcvalA[0] = sqrt(funcval);  
+                break; }}
+            
+            re_old = re;
+            /*printf("%f %i %i \n", re, ll, count); */
+            
+            /*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;
+            
+            if (ll == (iter-1)) {
+            Obj_func3D(A, D, P1, P2, P3,lambda, dimX, dimY, dimZ);
+            funcval = 0.0f; 
+            for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2);                           
+            funcvalA[0] = sqrt(funcval);            
+            }
+            
+        }
+        printf("FGP-TV iterations stopped at iteration %i with the function value %f \n", ll, funcvalA[0]);
+    }
+}
+
+/* 2D-case related Functions */
+/*****************************************************************/
+float Obj_func2D(float *A, float *D, float *R1, float *R2, 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++) {
+            /* boundary conditions  */
+            if (i == 0) {val1 = 0.0f;} else {val1 = R1[(i-1)*dimY + (j)];}
+            if (j == 0) {val2 = 0.0f;} 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);
+        }}
+    return *D;
+}
+float Grad_func2D(float *P1, float *P2, float *D, float *R1, float *R2, float lambda, int dimX, int dimY)
+{
+    float val1, val2, multip;
+    int i,j;
+    multip = (1.0f/(8.0f*lambda));
+#pragma omp parallel for shared(P1,P2,D,R1,R2,multip) private(i,j,val1,val2)
+    for(i=0; i<dimX; i++) {
+        for(j=0; j<dimY; j++) {
+            /* boundary conditions */
+            if (i == dimX-1) val1 = 0.0f; else val1 = D[(i)*dimY + (j)] - D[(i+1)*dimY + (j)];
+            if (j == dimY-1) val2 = 0.0f; else val2 = D[(i)*dimY + (j)] - D[(i)*dimY + (j+1)];
+            P1[(i)*dimY + (j)] = R1[(i)*dimY + (j)] + multip*val1;
+            P2[(i)*dimY + (j)] = R2[(i)*dimY + (j)] + multip*val2;
+        }}
+    return 1;
+}
+float Proj_func2D(float *P1, float *P2, int methTV, int dimX, int dimY)
+{
+    float val1, val2, denom;
+    int i,j;
+    if (methTV == 0) {
+        /* isotropic TV*/
+#pragma omp parallel for shared(P1,P2) private(i,j,denom)
+        for(i=0; i<dimX; i++) {
+            for(j=0; j<dimY; j++) {
+                denom = pow(P1[(i)*dimY + (j)],2) +  pow(P2[(i)*dimY + (j)],2);
+                if (denom > 1) {
+                    P1[(i)*dimY + (j)] = P1[(i)*dimY + (j)]/sqrt(denom);
+                    P2[(i)*dimY + (j)] = P2[(i)*dimY + (j)]/sqrt(denom);
+                }
+            }}
+    }
+    else {
+        /* anisotropic TV*/
+#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;
+    float multip;
+    multip = ((tk-1.0f)/tkp1);
+#pragma omp parallel for shared(P1,P2,P1_old,P2_old,R1,R2,multip) private(i,j)
+    for(i=0; i<dimX; i++) {
+        for(j=0; j<dimY; j++) {
+            R1[(i)*dimY + (j)] = P1[(i)*dimY + (j)] + multip*(P1[(i)*dimY + (j)] - P1_old[(i)*dimY + (j)]);
+            R2[(i)*dimY + (j)] = P2[(i)*dimY + (j)] + multip*(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++) {
+                /* boundary conditions */
+                if (i == 0) {val1 = 0.0f;} else {val1 = R1[(dimX*dimY)*k + (i-1)*dimY + (j)];}
+                if (j == 0) {val2 = 0.0f;} else {val2 = R2[(dimX*dimY)*k + (i)*dimY + (j-1)];}
+                if (k == 0) {val3 = 0.0f;} 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, multip;
+    int i,j,k;
+    multip = (1.0f/(8.0f*lambda));
+#pragma omp parallel for shared(P1,P2,P3,D,R1,R2,R3,multip) 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++) {
+                /* boundary conditions */
+                if (i == dimX-1) val1 = 0.0f; else val1 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*k + (i+1)*dimY + (j)];
+                if (j == dimY-1) val2 = 0.0f; else val2 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*k + (i)*dimY + (j+1)];
+                if (k == dimZ-1) val3 = 0.0f; 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)] + multip*val1;
+                P2[(dimX*dimY)*k + (i)*dimY + (j)] = R2[(dimX*dimY)*k + (i)*dimY + (j)] + multip*val2;
+                P3[(dimX*dimY)*k + (i)*dimY + (j)] = R3[(dimX*dimY)*k + (i)*dimY + (j)] + multip*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;
+    float multip;
+    multip = ((tk-1.0f)/tkp1);
+#pragma omp parallel for shared(P1,P2,P3,P1_old,P2_old,P3_old,R1,R2,R3,multip) 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)] + multip*(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)] + multip*(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)] + multip*(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;
+}
diff --git a/main_func/FISTA_REC.m b/main_func/FISTA_REC.m
index 79369a5..ed74181 100644
--- a/main_func/FISTA_REC.m
+++ b/main_func/FISTA_REC.m
@@ -1,34 +1,36 @@
-function [X,  error, objective, residual] = FISTA_REC(params)
+function [X,  output] = FISTA_REC(params)
 
-% <<<< FISTA-based reconstruction algorithm using ASTRA-toolbox (parallel beam) >>>>
+% <<<< FISTA-based reconstruction algorithm using ASTRA-toolbox >>>>
 % ___Input___:
 % params.[] file:
-%       - .sino (2D or 3D sinogram) [required]
-%       - .N (image dimension) [required]
-%       - .angles (in radians) [required]
+%       - .proj_geom (geometry of the projector) [required]
+%       - .vol_geom (geometry of the reconstructed object) [required]
+%       - .sino (vectorized in 2D or 3D sinogram) [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)
+%       - .weights (statisitcal weights, size of the 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)
+%       - .Regul_LambdaTV (TV regularization parameter, default 0 - reg. TV is switched off)
+%       - .Regul_tol (tolerance to terminate TV regularization, default 1.0e-04)
+%       - .Regul_iterTV (iterations for the TV penalty, default 0)
+%       - .Regul_LambdaHO (Higher Order LLT regularization parameter, default 0 - LLT reg. switched off)
+%       - .Regul_iterHO (iterations for HO penalty, default 50)
+%       - .Regul_tauHO (time step parameter for HO term)
+%       - .Ring_LambdaR_L1 (regularization parameter for L1 ring minimization, if lambdaR_L1 > 0 then switch on ring removal, default 0)
+%       - .Ring_Alpha (larger values can accelerate convergence but check stability, default 1)
 %       - .fidelity (choose between "LS" and "student" data fidelities)
+%       - .initializ (a 'warm start' using SIRT method from ASTRA)
 %       - .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)
+% 2. Resid_error - residual error (if X_ideal is given)
 % 3. value of the objective function
-% 4. forward projection(X)
+% 4. forward projection of X
+
 % References:
 % 1. "A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse
 % Problems" by A. Beck and M Teboulle
@@ -38,49 +40,53 @@ function [X,  error, objective, residual] = FISTA_REC(params)
 % 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.');
+if (isfield(params,'proj_geom') == 0)
+    error('%s \n', 'Please provide ASTRA projection geometry - proj_geom');
 else
-    fprintf('%s \n', 'Please provide a sinogram');
+    proj_geom = params.proj_geom;
 end
-if (isfield(params,'N'))
-    N = params.N;
+if (isfield(params,'vol_geom') == 0)
+    error('%s \n', 'Please provide ASTRA object geometry - vol_geom');
 else
-    fprintf('%s \n', 'Please provide N-size for the reconstructed image [N x N]');
+    vol_geom = params.vol_geom;
 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
+N = params.vol_geom.GridColCount;
+if (isfield(params,'sino'))
+    sino = params.sino;
+    [Detectors, anglesNumb, SlicesZ] = size(sino);
+    fprintf('%s %i %s %i %s %i %s \n', 'Sinogram has a dimension of', Detectors, 'detectors;', anglesNumb, 'projections;', SlicesZ, 'vertical slices.');
 else
-    fprintf('%s \n', 'Please provide a vector of angles');
+    error('%s \n', 'Please provide a sinogram');
 end
 if (isfield(params,'iterFISTA'))
     iterFISTA = params.iterFISTA;
 else
     iterFISTA = 30;
 end
+if (isfield(params,'weights'))
+    weights = params.weights;
+else
+    weights = ones(size(sino));
+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);
+    niter = 5; % number of iteration for PM
+    x = rand(N,N,SlicesZ);
+    sqweight = sqrt(weights);
+    [sino_id, y] = astra_create_sino3d_cuda(x, proj_geom, vol_geom);
+    y = sqweight.*y;
+    astra_mex_data3d('delete', sino_id);
     
     for i = 1:niter
-        x = astra_create_backprojection_cuda(y, proj_geom, vol_geom);
-        s = norm(x);
+        [id,x] = astra_create_backprojection3d_cuda(sqweight.*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);
+        [sino_id, y] = astra_create_sino3d_cuda(x, proj_geom, vol_geom);
+        y = sqweight.*y;
+        astra_mex_data3d('delete', sino_id);
+        astra_mex_data3d('delete', id);
     end
     L_const = s;
 end
@@ -89,53 +95,48 @@ if (isfield(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;
+if (isfield(params,'Regul_LambdaTV'))
+    lambdaTV = params.Regul_LambdaTV;
 else
     lambdaTV = 0;
 end
-if (isfield(params,'tol'))
-    tol = params.tol;
+if (isfield(params,'Regul_tol'))
+    tol = params.Regul_tol;
 else
     tol = 1.0e-04;
 end
-if (isfield(params,'iterTV'))
-    iterTV = params.iterTV;
+if (isfield(params,'Regul_iterTV'))
+    iterTV = params.Regul_iterTV;
 else
-    iterTV = 10;
+    iterTV = 25;
 end
-if (isfield(params,'lambdaHO'))
-    lambdaHO = params.lambdaHO;
+if (isfield(params,'Regul_LambdaHO'))
+    lambdaHO = params.Regul_LambdaHO;
 else
     lambdaHO = 0;
 end
-if (isfield(params,'iterHO'))
-    iterHO = params.iterHO;
+if (isfield(params,'Regul_iterHO'))
+    iterHO = params.Regul_iterHO;
 else
     iterHO = 50;
 end
-if (isfield(params,'tauHO'))
-    tauHO = params.tauHO;
+if (isfield(params,'Regul_tauHO'))
+    tauHO = params.Regul_tauHO;
 else
     tauHO = 0.0001;
 end
-if (isfield(params,'lambdaR_L1'))
-    lambdaR_L1 = params.lambdaR_L1;    
+if (isfield(params,'Ring_LambdaR_L1'))
+    lambdaR_L1 = params.Ring_LambdaR_L1;
 else
     lambdaR_L1 = 0;
 end
-if (isfield(params,'alpha_ring'))    
-    alpha_ring = params.alpha_ring; % higher values can accelerate ring removal procedure
+if (isfield(params,'Ring_Alpha'))
+    alpha_ring = params.Ring_Alpha; % higher values can accelerate ring removal procedure
 else
     alpha_ring = 1;
 end
@@ -164,21 +165,43 @@ if (isfield(params,'slice'))
 else
     slice = 1;
 end
+if (isfield(params,'initilize'))
+    % Create a data object for the reconstruction
+    rec_id = astra_mex_data3d('create', '-vol', vol_geom);
+    
+    sinogram_id = astra_mex_data3d('create', '-proj3d', proj_geom, sino);
+    
+    % Set up the parameters for a reconstruction algorithm using the GPU
+    cfg = astra_struct('SIRT3D_CUDA');
+    cfg.ReconstructionDataId = rec_id;
+    cfg.ProjectionDataId = sinogram_id;
+    
+    % Create the algorithm object from the configuration structure
+    alg_id = astra_mex_algorithm('create', cfg);
+    astra_mex_algorithm('iterate', alg_id, 35);
+    % Get the result
+    X = astra_mex_data3d('get', rec_id);
+    
+    % Clean up. Note that GPU memory is tied up in the algorithm object,
+    % and main RAM in the data objects.
+    astra_mex_algorithm('delete', alg_id);
+    astra_mex_data3d('delete', rec_id);
+    astra_mex_data3d('delete', sinogram_id);
+else
+    X = zeros(N,N,SlicesZ, 'single'); % storage for the solution
+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
+Resid_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
+    add_ring = zeros(size(sino),'single'); % size of sinogram array
     r = zeros(Detectors,SlicesZ, 'single'); % 2D array (for 3D data) of sparse "ring" vectors
     r_x = r;
     
@@ -189,47 +212,40 @@ if (lambdaR_L1 > 0)
         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);
+        [sino_id, sino_updt] = astra_create_sino3d_cuda(X_t, proj_geom, vol_geom);
+        
+        for kkk = 1:anglesNumb
+            add_ring(:,kkk,:) =  sino(:,kkk,:) - alpha_ring.*r_x;
+        end
+        
+        residual =  weights.*(sino_updt - add_ring);
+        
+        if (precondition == 1)
+            residual = filtersinc(residual'); % filtering residual (Fourier preconditioning)
+            residual = residual';
         end
         
+        vec = sum(residual,2);
+        
+        r = r_x - (1./L_const).*vec;
+        
+        [id, x_temp] = astra_create_backprojection3d_cuda(residual, proj_geom, vol_geom);
+        
+        X = X_t - (1/L_const).*x_temp;
+        astra_mex_data3d('delete', sino_id);
+        astra_mex_data3d('delete', id);
+        
         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, f_val] = FGP_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA
+            objective(i) = 0.5.*norm(residual(:))^2 + f_val;
             %       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
+            X1 = FGP_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA
+            X2 = LLT_model(single(X), lambdaHO, tauHO, iterHO, 3.0e-05, 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;
@@ -244,11 +260,11 @@ if (lambdaR_L1 > 0)
         if (show == 1)
             figure(10); imshow(X(:,:,slice), [0 maxvalplot]);
             figure(11); plot(r); title('Rings offset vector')
-            pause(0.03);            
+            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));
+            Resid_error(i) = RMSE(X(ROI), X_ideal(ROI));
+            fprintf('%s %i %s %s %.4f  %s %s %.4f \n', 'Iteration Number:', i, '|', 'Error RMSE:', Resid_error(i), '|', 'Objective:', objective(i));
         else
             fprintf('%s %i  %s %s %.4f \n', 'Iteration Number:', i, '|', 'Objective:', objective(i));
         end
@@ -258,50 +274,42 @@ if (lambdaR_L1 > 0)
 else
     % WITHOUT ring removal
     t = 1;
-    X = zeros(N,N,SlicesZ, 'single');
     X_t = X;
     
-    % iterations loop
+    % FISTA outer 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);
+        [sino_id, sino_updt] = astra_create_sino3d_cuda(X_t, proj_geom, vol_geom);
+        residual = weights.*(sino_updt - sino);
+        
+        % employ students t fidelity term
+        if (strcmp(fidelity,'student') == 1)
+            res_vec = reshape(residual, anglesNumb*Detectors*SlicesZ,1);
+            %s = 100;
+            %gr = (2)*res_vec./(s*2 + conj(res_vec).*res_vec);
+            [ff, gr] = studentst(res_vec,1);
+            residual = reshape(gr, Detectors, anglesNumb, SlicesZ);
+        end
+        
+        if (precondition == 1)
+            residual = filtersinc(residual'); % filtering residual (Fourier preconditioning)
+            residual = residual';
         end
         
+        [id, x_temp] = astra_create_backprojection3d_cuda(residual, proj_geom, vol_geom);
+        X = X_t - (1/L_const).*x_temp;
+        astra_mex_data3d('delete', sino_id);
+        astra_mex_data3d('delete', id);
+        
         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
+            [X,f_val] = FGP_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA
             if (strcmp(fidelity,'student') == 1)
-                objective(i) = ff + norm(gradTV(:));
+                objective(i) = ff + f_val;
             else
-                objective(i) = 0.5.*norm(residual(:))^2 + norm(gradTV(:));
+                objective(i) = 0.5.*norm(residual(:))^2 + f_val;
             end
             %  X = SplitBregman_TV(single(X), lambdaTV, iterTV, tol);  % TV-Split Bregman regularization on CPU (memory limited)
         elseif ((lambdaHO > 0) && (lambdaTV == 0))
@@ -315,24 +323,25 @@ else
             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);            
+            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));
+            Resid_error(i) = RMSE(X(ROI), X_ideal(ROI));
+            fprintf('%s %i %s %s %.4f  %s %s %.4f \n', 'Iteration Number:', i, '|', 'Error RMSE:', Resid_error(i), '|', 'Objective:', objective(i));
         else
             fprintf('%s %i  %s %s %.4f \n', 'Iteration Number:', i, '|', 'Objective:', objective(i));
         end
         
-        
     end
     
 end
+output.Resid_error = Resid_error;
+output.objective = objective;
+output.L_const = L_const;
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 end
diff --git a/main_func/FISTA_TV.c b/main_func/FISTA_TV.c
deleted file mode 100644
index 87681bc..0000000
--- a/main_func/FISTA_TV.c
+++ /dev/null
@@ -1,331 +0,0 @@
-#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
index a611e54..0aed31e 100644
--- a/main_func/LLT_model.c
+++ b/main_func/LLT_model.c
@@ -6,7 +6,7 @@
 #include <stdio.h>
 #include "omp.h"
 
-#define EPS 0.001
+#define EPS 0.01
 
 /* C-OMP implementation of Lysaker, Lundervold and Tai (LLT) model of higher order regularization penalty
  *
diff --git a/main_func/SplitBregman_TV.c b/main_func/SplitBregman_TV.c
index 691ccce..f143aa6 100644
--- a/main_func/SplitBregman_TV.c
+++ b/main_func/SplitBregman_TV.c
@@ -11,8 +11,9 @@
  * Input Parameters:
  * 1. Noisy image/volume
  * 2. lambda - regularization parameter
- * 3. Number of iterations
- * 4. eplsilon - tolerance constant
+ * 3. Number of iterations [OPTIONAL parameter]
+ * 4. eplsilon - tolerance constant [OPTIONAL parameter]
+ * 5. TV-type: 'iso' or 'l1' [OPTIONAL parameter]
  *
  * Output:
  * Filtered/regularized image
@@ -31,12 +32,13 @@
 
 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 updDxDy_shrinkIso2D(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 updDxDyDz_shrinkAniso3D(float *U, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ, float lambda);
+float updDxDyDz_shrinkIso3D(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(
@@ -44,28 +46,39 @@ void mexFunction(
         int nrhs, const mxArray *prhs[])
         
 {
-    int number_of_dims, iter, dimX, dimY, dimZ, ll, j, count;
+    int number_of_dims, iter, dimX, dimY, dimZ, ll, j, count, methTV;
     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*/
+    if ((nrhs < 2) || (nrhs > 5)) mexErrMsgTxt("At least 2 parameters is required: Image(2D/3D), Regularization parameter. The full list of parameters: Image(2D/3D), Regularization parameter, iterations number, tolerance, penalty type ('iso' or 'l1')");
     
     /*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 */
+    iter = 35; /* default iterations number */
+    epsil = 0.0001; /* default tolerance constant */
+    methTV = 0;  /* default isotropic TV penalty */
+    if ((nrhs == 3) || (nrhs == 4) || (nrhs == 5))  iter = (int) mxGetScalar(prhs[2]); /* iterations number */
+    if ((nrhs == 4) || (nrhs == 5))  epsil =  (float) mxGetScalar(prhs[3]); /* tolerance constant */
+    if (nrhs == 5)  {
+        char *penalty_type;
+        penalty_type = mxArrayToString(prhs[4]); /* choosing TV penalty: 'iso' or 'l1', 'iso' is the default */
+        if ((strcmp(penalty_type, "l1") != 0) && (strcmp(penalty_type, "iso") != 0)) mexErrMsgTxt("Choose TV type: 'iso' or 'l1',");
+        if (strcmp(penalty_type, "l1") == 0)  methTV = 1;  /* enable 'l1' penalty */
+        mxFree(penalty_type);
+    }
+    if (mxGetClassID(prhs[0]) != mxSINGLE_CLASS) {mexErrMsgTxt("The input image must be in a single precision"); }
     
-    lambda = 2.0f*2.0f;
+    lambda = 2.0f*mu;
     count = 1;
-    re_old = 0.0f;   
+    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));
@@ -73,7 +86,7 @@ void mexFunction(
         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));       
+        By = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
         
         copyIm(A, U, dimX, dimY, dimZ); /*initialize */
         
@@ -82,13 +95,14 @@ void mexFunction(
             
             /*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);                    
+            /*GS iteration */
+            gauss_seidel2D(U, A, Dx, Dy, Bx, By, dimX, dimY, lambda, mu);
+            
+            if (methTV == 1)  updDxDy_shrinkAniso2D(U, Dx, Dy, Bx, By, dimX, dimY, lambda);
+            else updDxDy_shrinkIso2D(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;
@@ -97,20 +111,20 @@ void mexFunction(
                 re += pow(U_old[j] - U[j],2);
                 re1 += pow(U_old[j],2);
             }
-            re = sqrt(re)/sqrt(re1);           
+            re = sqrt(re)/sqrt(re1);
             if (re < epsil)  count++;
-            if (count > 4) break;            
+            if (count > 4) break;
             
             /* check that the residual norm is decreasing */
             if (ll > 2) {
-                if (re > re_old) break; 
+                if (re > re_old) break;
             }
-            re_old = re;               
-            /*printf("%f %i %i \n", re, ll, count); */            
+            re_old = re;
+            /*printf("%f %i %i \n", re, ll, count); */
             
-           /*copyIm(U_old, U, dimX, dimY, dimZ); */
+            /*copyIm(U_old, U, dimX, dimY, dimZ); */
         }
-        printf("SB iterations stopped at iteration: %i\n", ll);   
+        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));
@@ -119,22 +133,24 @@ void mexFunction(
         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));       
+        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);
+            /*storing old values*/
+            copyIm(U, U_old, dimX, dimY, dimZ);
+            
+            /*GS iteration */
+            gauss_seidel3D(U, A, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ, lambda, mu);
+            
+            if (methTV == 1) updDxDyDz_shrinkAniso3D(U, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ, lambda);
+            else updDxDyDz_shrinkIso3D(U, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ, lambda);
             
-        updBxByBz3D(U, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ);                    
+            updBxByBz3D(U, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ);
             
             /* calculate norm to terminate earlier */
             re = 0.0f; re1 = 0.0f;
@@ -143,17 +159,17 @@ void mexFunction(
                 re += pow(U[j] - U_old[j],2);
                 re1 += pow(U[j],2);
             }
-            re = sqrt(re)/sqrt(re1);           
+            re = sqrt(re)/sqrt(re1);
             if (re < epsil)  count++;
-            if (count > 4) break;            
+            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;                       
+            re_old = re;
         }
-        printf("SB iterations stopped at iteration: %i\n", ll);        
+        printf("SB iterations stopped at iteration: %i\n", ll);
     }
 }
 
@@ -167,92 +183,92 @@ float gauss_seidel2D(float *U, float *A, float *Dx, float *Dy, float *Bx, float
     
 #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;
+        /* 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) */           
+            /* symmetric boundary conditions (Neuman) */
             j1 = j+1; if (j1 == dimY) j1 = j-1;
-            j2 = j-1; if (j2 < 0) j2 = 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 = 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)];			
+            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) 
+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, val22;
-   
-   #pragma omp parallel for shared(U) private(i,j,i1,j1,val1,val11,val2,val22)
-   for(i=0; i<dimX; i++) {
+    int i,j,i1,j1;
+    float val1, val11, val2, val22, denom_lam;
+    denom_lam = 1.0f/lambda;
+#pragma omp parallel for shared(U,denom_lam) 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;             
+            val11 = fabs(val1) - denom_lam; if (val11 < 0) val11 = 0;
+            val22 = fabs(val2) - denom_lam; 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) 
+float updDxDy_shrinkIso2D(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++) {
+    int i,j,i1,j1;
+    float val1, val11, val2, denom, denom_lam;
+    denom_lam = 1.0f/lambda;
+    
+#pragma omp parallel for shared(U,denom_lam) private(i,j,i1,j1,val1,val11,val2,denom)
+    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;             
-                        
+            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); 
-            }            
+                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++) {
+    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;                  
+            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;
+            By[(i)*dimY + (j)] = By[(i)*dimY + (j)] + ((U[(i)*dimY + (j1)] - U[(i)*dimY + (j)]) - Dy[(i)*dimY + (j)]);
+        }}
+    return 1;
 }
 
 
@@ -261,78 +277,115 @@ float updBxBy2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX,
 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;    
+    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;   
+                /* 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)
+float updDxDyDz_shrinkAniso3D(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++) {
+    int i,j,i1,j1,k,k1,index;
+    float val1, val11, val2, val22, val3, val33, denom_lam;
+    denom_lam = 1.0f/lambda;
+#pragma omp parallel for shared(U,denom_lam) private(index,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;
-            
-        }}}
+                index = (dimX*dimY)*k + (i)*dimY + (j);
+                /* 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[index]) + Bx[index];
+                val2 = (U[(dimX*dimY)*k + (i)*dimY + (j1)] - U[index]) + By[index];
+                val3 = (U[(dimX*dimY)*k1 + (i)*dimY + (j)] - U[index]) + Bz[index];
+                
+                val11 = fabs(val1) - denom_lam; if (val11 < 0) val11 = 0;
+                val22 = fabs(val2) - denom_lam; if (val22 < 0) val22 = 0;
+                val33 = fabs(val3) - denom_lam; if (val33 < 0) val33 = 0;
+                
+                if (val1 !=0) Dx[index] = (val1/fabs(val1))*val11; else Dx[index] = 0;
+                if (val2 !=0) Dy[index] = (val2/fabs(val2))*val22; else Dy[index] = 0;
+                if (val3 !=0) Dz[index] = (val3/fabs(val3))*val33; else Dz[index] = 0;
+                
+            }}}
+    return 1;
+}
+float updDxDyDz_shrinkIso3D(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,index;
+    float val1, val11, val2, val3, denom, denom_lam;
+    denom_lam = 1.0f/lambda;
+#pragma omp parallel for shared(U,denom_lam) private(index,denom,i,j,i1,j1,k,k1,val1,val11,val2,val3)
+    for(i=0; i<dimX; i++) {
+        for(j=0; j<dimY; j++) {
+            for(k=0; k<dimZ; k++) {
+                index = (dimX*dimY)*k + (i)*dimY + (j);
+                /* 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[index]) + Bx[index];
+                val2 = (U[(dimX*dimY)*k + (i)*dimY + (j1)] - U[index]) + By[index];
+                val3 = (U[(dimX*dimY)*k1 + (i)*dimY + (j)] - U[index]) + Bz[index];
+                
+                denom = sqrt(val1*val1 + val2*val2 + val3*val3);
+                
+                val11 = (denom - denom_lam); if (val11 < 0) val11 = 0.0f;
+                
+                if (denom != 0.0f) {
+                    Dx[index] = val11*(val1/denom);
+                    Dy[index] = val11*(val2/denom);
+                    Dz[index] = val11*(val3/denom);
+                }
+                else {
+                    Dx[index] = 0;
+                    Dy[index] = 0;
+                    Dz[index] = 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++) {
+    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;
+                /* 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 */
 /*****************************************************************/
diff --git a/main_func/compile_mex.m b/main_func/compile_mex.m
index ea6e3a5..4d97bc2 100644
--- a/main_func/compile_mex.m
+++ b/main_func/compile_mex.m
@@ -1,4 +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
+mex FGP_TV.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp"
+mex SplitBregman_TV.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp"
diff --git a/main_func/studentst.m b/main_func/studentst.m
index 99fed1e..93e0a0a 100644
--- a/main_func/studentst.m
+++ b/main_func/studentst.m
@@ -1,47 +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);
+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);
-- 
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