From 5d4464a78d1807565a75c9430cfe5e6857fe9232 Mon Sep 17 00:00:00 2001
From: Daniil Kazantsev <dkazanc@hotmail.com>
Date: Mon, 31 Jul 2017 23:57:08 +0100
Subject: New regularizers for FISTA
---
main_func/FGP_TV.c | 400 ------------------------
main_func/FISTA_REC.m | 100 +++---
main_func/LLT_model.c | 431 --------------------------
main_func/SplitBregman_TV.c | 399 ------------------------
main_func/compile_mex.m | 8 +-
main_func/regularizers_CPU/FGP_TV.c | 400 ++++++++++++++++++++++++
main_func/regularizers_CPU/LLT_model.c | 431 ++++++++++++++++++++++++++
main_func/regularizers_CPU/PatchBased_Regul.c | 295 ++++++++++++++++++
main_func/regularizers_CPU/SplitBregman_TV.c | 399 ++++++++++++++++++++++++
main_func/regularizers_CPU/TGV_PD.c | 353 +++++++++++++++++++++
10 files changed, 1943 insertions(+), 1273 deletions(-)
delete mode 100644 main_func/FGP_TV.c
delete mode 100644 main_func/LLT_model.c
delete mode 100644 main_func/SplitBregman_TV.c
create mode 100644 main_func/regularizers_CPU/FGP_TV.c
create mode 100644 main_func/regularizers_CPU/LLT_model.c
create mode 100644 main_func/regularizers_CPU/PatchBased_Regul.c
create mode 100644 main_func/regularizers_CPU/SplitBregman_TV.c
create mode 100644 main_func/regularizers_CPU/TGV_PD.c
(limited to 'main_func')
diff --git a/main_func/FGP_TV.c b/main_func/FGP_TV.c
deleted file mode 100644
index 1a1fd13..0000000
--- a/main_func/FGP_TV.c
+++ /dev/null
@@ -1,400 +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 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 db2b581..2823691 100644
--- a/main_func/FISTA_REC.m
+++ b/main_func/FISTA_REC.m
@@ -15,7 +15,6 @@ function [X, output] = FISTA_REC(params)
%----------------Regularization choices------------------------
% - .Regul_Lambda_FGPTV (FGP-TV regularization parameter)
% - .Regul_Lambda_SBTV (SplitBregman-TV regularization parameter)
-% - .Regul_Lambda_L1 (L1 regularization by soft-thresholding)
% - .Regul_Lambda_TVLLT (Higher order SB-LLT regularization parameter)
% - .Regul_tol (tolerance to terminate regul iterations, default 1.0e-04)
% - .Regul_Iterations (iterations for the selected penalty, default 25)
@@ -28,7 +27,7 @@ function [X, output] = FISTA_REC(params)
% - .slice (for 3D volumes - slice number to imshow)
% ___Output___:
% 1. X - reconstructed image/volume
-% 2. output - structure with
+% 2. output - a structure with
% - .Resid_error - residual error (if X_ideal is given)
% - .objective: value of the objective function
% - .L_const: Lipshitz constant to avoid recalculations
@@ -74,21 +73,50 @@ if (isfield(params,'L_const'))
L_const = params.L_const;
else
% using Power method (PM) to establish L constant
- niter = 8; % 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
- [id,x] = astra_create_backprojection3d_cuda(sqweight.*y, proj_geom, vol_geom);
- s = norm(x(:));
- x = x/s;
- [sino_id, y] = astra_create_sino3d_cuda(x, proj_geom, vol_geom);
+ if (strcmp(proj_geom.type,'parallel') || strcmp(proj_geom.type,'parallel3d'))
+ % for parallel geometry we can do just one slice
+ fprintf('%s \n', 'Calculating Lipshitz constant for parallel beam geometry...');
+ niter = 15; % number of iteration for the PM
+ x1 = rand(N,N,1);
+ sqweight = sqrt(weights(:,:,1));
+ proj_geomT = proj_geom;
+ proj_geomT.DetectorRowCount = 1;
+ vol_geomT = vol_geom;
+ vol_geomT.GridSliceCount = 1;
+ [sino_id, y] = astra_create_sino3d_cuda(x1, proj_geomT, vol_geomT);
y = sqweight.*y;
astra_mex_data3d('delete', sino_id);
- astra_mex_data3d('delete', id);
+
+ for i = 1:niter
+ [id,x1] = astra_create_backprojection3d_cuda(sqweight.*y, proj_geomT, vol_geomT);
+ s = norm(x1(:));
+ x1 = x1/s;
+ [sino_id, y] = astra_create_sino3d_cuda(x1, proj_geomT, vol_geomT);
+ y = sqweight.*y;
+ astra_mex_data3d('delete', sino_id);
+ astra_mex_data3d('delete', id);
+ end
+ clear proj_geomT vol_geomT
+ else
+ % divergen beam geometry
+ fprintf('%s \n', 'Calculating Lipshitz constant for divergen beam geometry...');
+ niter = 8; % number of iteration for PM
+ x1 = rand(N,N,SlicesZ);
+ sqweight = sqrt(weights);
+ [sino_id, y] = astra_create_sino3d_cuda(x1, proj_geom, vol_geom);
+ y = sqweight.*y;
+ astra_mex_data3d('delete', sino_id);
+
+ for i = 1:niter
+ [id,x1] = astra_create_backprojection3d_cuda(sqweight.*y, proj_geom, vol_geom);
+ s = norm(x1(:));
+ x1 = x1/s;
+ [sino_id, y] = astra_create_sino3d_cuda(x1, proj_geom, vol_geom);
+ y = sqweight.*y;
+ astra_mex_data3d('delete', sino_id);
+ astra_mex_data3d('delete', id);
+ end
+ clear x1
end
L_const = s;
end
@@ -112,11 +140,6 @@ if (isfield(params,'Regul_Lambda_SBTV'))
else
lambdaSB_TV = 0;
end
-if (isfield(params,'Regul_Lambda_L1'))
- lambdaL1 = params.Regul_Lambda_L1;
-else
- lambdaL1 = 0;
-end
if (isfield(params,'Regul_tol'))
tol = params.Regul_tol;
else
@@ -194,19 +217,18 @@ else
X = zeros(N,N,SlicesZ, 'single'); % storage for the solution
end
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-Resid_error = zeros(iterFISTA,1); % error vector
-objective = zeros(iterFISTA,1); % obhective vector
+%----------------Reconstruction part------------------------
+Resid_error = zeros(iterFISTA,1); % errors vector (if the ground truth is given)
+objective = zeros(iterFISTA,1); % objective function values vector
t = 1;
X_t = X;
-% 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; % another ring variable
residual = zeros(size(sino),'single');
-% Outer iterations loop
+% Outer FISTA iterations loop
for i = 1:iterFISTA
X_old = X;
@@ -216,12 +238,10 @@ for i = 1:iterFISTA
[sino_id, sino_updt] = astra_create_sino3d_cuda(X_t, proj_geom, vol_geom);
if (lambdaR_L1 > 0)
- % add ring removal part (Group-Huber fidelity)
+ % ring removal part (Group-Huber fidelity)
for kkk = 1:anglesNumb
- % add_ring(:,kkk,:) = squeeze(sino(:,kkk,:)) - alpha_ring.*r_x;
residual(:,kkk,:) = squeeze(weights(:,kkk,:)).*(squeeze(sino_updt(:,kkk,:)) - (squeeze(sino(:,kkk,:)) - alpha_ring.*r_x));
- end
-
+ end
vec = sum(residual,2);
if (SlicesZ > 1)
vec = squeeze(vec(:,1,:));
@@ -229,9 +249,10 @@ for i = 1:iterFISTA
r = r_x - (1./L_const).*vec;
else
% no ring removal
- residual = weights.*(sino_updt - sino);
+ residual = weights.*(sino_updt - sino);
end
- % residual = weights.*(sino_updt - add_ring);
+
+ objective(i) = (0.5*norm(residual(:))^2)/(Detectors*anglesNumb*SlicesZ); % for the objective function output
[id, x_temp] = astra_create_backprojection3d_cuda(residual, proj_geom, vol_geom);
@@ -242,27 +263,22 @@ for i = 1:iterFISTA
if (lambdaFGP_TV > 0)
% FGP-TV regularization
[X, f_val] = FGP_TV(single(X), lambdaFGP_TV, IterationsRegul, tol, 'iso');
- objective(i) = 0.5.*norm(residual(:))^2 + f_val;
+ objective(i) = objective(i) + f_val;
end
if (lambdaSB_TV > 0)
% Split Bregman regularization
X = SplitBregman_TV(single(X), lambdaSB_TV, IterationsRegul, tol); % (more memory efficent)
- objective(i) = 0.5.*norm(residual(:))^2;
- end
- if (lambdaL1 > 0)
- % L1 soft-threhsolding regularization
- X = max(abs(X)-lambdaL1, 0).*sign(X);
- objective(i) = 0.5.*norm(residual(:))^2;
end
if (lambdaHO > 0)
% Higher Order (LLT) regularization
X2 = LLT_model(single(X), lambdaHO, tauHO, iterHO, 3.0e-05, 0);
X = 0.5.*(X + X2); % averaged combination of two solutions
- objective(i) = 0.5.*norm(residual(:))^2;
end
+
+
if (lambdaR_L1 > 0)
- r = max(abs(r)-lambdaR_L1, 0).*sign(r); % soft-thresholding operator
+ r = max(abs(r)-lambdaR_L1, 0).*sign(r); % soft-thresholding operator for ring vector
end
t = (1 + sqrt(1 + 4*t^2))/2; % updating t
@@ -281,9 +297,9 @@ for i = 1:iterFISTA
end
if (strcmp(X_ideal, 'none' ) == 0)
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));
+ fprintf('%s %i %s %s %.4f %s %s %f \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));
+ fprintf('%s %i %s %s %f \n', 'Iteration Number:', i, '|', 'Objective:', objective(i));
end
end
output.Resid_error = Resid_error;
diff --git a/main_func/LLT_model.c b/main_func/LLT_model.c
deleted file mode 100644
index 0aed31e..0000000
--- a/main_func/LLT_model.c
+++ /dev/null
@@ -1,431 +0,0 @@
-#include "mex.h"
-#include <matrix.h>
-#include <math.h>
-#include <stdlib.h>
-#include <memory.h>
-#include <stdio.h>
-#include "omp.h"
-
-#define EPS 0.01
-
-/* 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
deleted file mode 100644
index f143aa6..0000000
--- a/main_func/SplitBregman_TV.c
+++ /dev/null
@@ -1,399 +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 Split Bregman - TV denoising-regularization model (2D/3D)
- *
- * Input Parameters:
- * 1. Noisy image/volume
- * 2. lambda - regularization parameter
- * 3. Number of iterations [OPTIONAL parameter]
- * 4. eplsilon - tolerance constant [OPTIONAL parameter]
- * 5. TV-type: 'iso' or 'l1' [OPTIONAL parameter]
- *
- * 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_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_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(
- 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, *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]);
-
- /*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 = 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*mu;
- 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);
-
- /*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;
- 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);
-
- /*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);
-
- /* 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_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, 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) - 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_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,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;
-
- 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_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,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++) {
- 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++) {
- 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
index 4d97bc2..7bfa8eb 100644
--- a/main_func/compile_mex.m
+++ b/main_func/compile_mex.m
@@ -1,4 +1,10 @@
-% compile mex's
+% compile mex's once
+cd regularizers_CPU/
+
mex LLT_model.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp"
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"
+mex TGV_PD.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp"
+
+cd ../../
+cd demos
diff --git a/main_func/regularizers_CPU/FGP_TV.c b/main_func/regularizers_CPU/FGP_TV.c
new file mode 100644
index 0000000..1a1fd13
--- /dev/null
+++ b/main_func/regularizers_CPU/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/regularizers_CPU/LLT_model.c b/main_func/regularizers_CPU/LLT_model.c
new file mode 100644
index 0000000..0aed31e
--- /dev/null
+++ b/main_func/regularizers_CPU/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 0.01
+
+/* 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/regularizers_CPU/PatchBased_Regul.c b/main_func/regularizers_CPU/PatchBased_Regul.c
new file mode 100644
index 0000000..1ed29d4
--- /dev/null
+++ b/main_func/regularizers_CPU/PatchBased_Regul.c
@@ -0,0 +1,295 @@
+#define _USE_MATH_DEFINES
+
+#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 patch-based (PB) regularization (2D and 3D cases).
+ * This method finds self-similar patches in data and performs one fixed point iteration to mimimize the PB penalty function
+ *
+ * References: 1. Yang Z. & Jacob M. "Nonlocal Regularization of Inverse Problems"
+ * 2. Kazantsev D. et al. "4D-CT reconstruction with unified spatial-temporal patch-based regularization"
+ *
+ * Input Parameters (mandatory):
+ * 1. Image (2D or 3D)
+ * 2. ratio of the searching window (e.g. 3 = (2*3+1) = 7 pixels window)
+ * 3. ratio of the similarity window (e.g. 1 = (2*1+1) = 3 pixels window)
+ * 4. h - parameter for the PB penalty function
+ * 5. lambda - regularization parameter
+
+ * Output:
+ * 1. regularized (denoised) Image (N x N)/volume (N x N x N)
+ *
+ * Quick 2D denoising example in Matlab:
+ Im = double(imread('lena_gray_256.tif'))/255; % loading image
+ u0 = Im + .03*randn(size(Im)); u0(u0<0) = 0; % adding noise
+ ImDen = PB_Regul_CPU(single(u0), 3, 1, 0.08, 0.05);
+ *
+ * Please see more tests in a file:
+ TestTemporalSmoothing.m
+
+ *
+ * Matlab + C/mex compilers needed
+ * to compile with OMP support: mex PB_Regul_CPU.c CFLAGS="\$CFLAGS -fopenmp -Wall" LDFLAGS="\$LDFLAGS -fopenmp"
+ *
+ * D. Kazantsev *
+ * 02/07/2014
+ * Harwell, UK
+ */
+
+float pad_crop(float *A, float *Ap, int OldSizeX, int OldSizeY, int OldSizeZ, int NewSizeX, int NewSizeY, int NewSizeZ, int padXY, int switchpad_crop);
+float PB_FUNC2D(float *A, float *B, int dimX, int dimY, int padXY, int SearchW, int SimilW, float h, float lambda);
+float PB_FUNC3D(float *A, float *B, int dimX, int dimY, int dimZ, int padXY, int SearchW, int SimilW, float h, float lambda);
+
+void mexFunction(
+ int nlhs, mxArray *plhs[],
+ int nrhs, const mxArray *prhs[])
+{
+ int N, M, Z, numdims, SearchW, SimilW, SearchW_real, padXY, newsizeX, newsizeY, newsizeZ, switchpad_crop;
+ const int *dims;
+ float *A, *B=NULL, *Ap=NULL, *Bp=NULL, h, lambda;
+
+ numdims = mxGetNumberOfDimensions(prhs[0]);
+ dims = mxGetDimensions(prhs[0]);
+
+ N = dims[0];
+ M = dims[1];
+ Z = dims[2];
+
+ if ((numdims < 2) || (numdims > 3)) {mexErrMsgTxt("The input should be 2D image or 3D volume");}
+ if (mxGetClassID(prhs[0]) != mxSINGLE_CLASS) {mexErrMsgTxt("The input in single precision is required"); }
+
+ if(nrhs != 5) mexErrMsgTxt("Five inputs reqired: Image(2D,3D), SearchW, SimilW, Threshold, Regularization parameter");
+
+ /*Handling inputs*/
+ A = (float *) mxGetData(prhs[0]); /* the image to regularize/filter */
+ SearchW_real = (int) mxGetScalar(prhs[1]); /* the searching window ratio */
+ SimilW = (int) mxGetScalar(prhs[2]); /* the similarity window ratio */
+ h = (float) mxGetScalar(prhs[3]); /* parameter for the PB filtering function */
+ lambda = (float) mxGetScalar(prhs[4]); /* regularization parameter */
+
+ if (h <= 0) mexErrMsgTxt("Parmeter for the PB penalty function should be > 0");
+ if (lambda <= 0) mexErrMsgTxt(" Regularization parmeter should be > 0");
+
+ SearchW = SearchW_real + 2*SimilW;
+
+ /* SearchW_full = 2*SearchW + 1; */ /* the full searching window size */
+ /* SimilW_full = 2*SimilW + 1; */ /* the full similarity window size */
+
+
+ padXY = SearchW + 2*SimilW; /* padding sizes */
+ newsizeX = N + 2*(padXY); /* the X size of the padded array */
+ newsizeY = M + 2*(padXY); /* the Y size of the padded array */
+ newsizeZ = Z + 2*(padXY); /* the Z size of the padded array */
+ int N_dims[] = {newsizeX, newsizeY, newsizeZ};
+
+ /******************************2D case ****************************/
+ if (numdims == 2) {
+ /*Handling output*/
+ B = (float*)mxGetData(plhs[0] = mxCreateNumericMatrix(N, M, mxSINGLE_CLASS, mxREAL));
+ /*allocating memory for the padded arrays */
+ Ap = (float*)mxGetData(mxCreateNumericMatrix(newsizeX, newsizeY, mxSINGLE_CLASS, mxREAL));
+ Bp = (float*)mxGetData(mxCreateNumericMatrix(newsizeX, newsizeY, mxSINGLE_CLASS, mxREAL));
+ /**************************************************************************/
+ /*Perform padding of image A to the size of [newsizeX * newsizeY] */
+ switchpad_crop = 0; /*padding*/
+ pad_crop(A, Ap, M, N, 0, newsizeY, newsizeX, 0, padXY, switchpad_crop);
+
+ /* Do PB regularization with the padded array */
+ PB_FUNC2D(Ap, Bp, newsizeY, newsizeX, padXY, SearchW, SimilW, (float)h, (float)lambda);
+
+ switchpad_crop = 1; /*cropping*/
+ pad_crop(Bp, B, M, N, 0, newsizeY, newsizeX, 0, padXY, switchpad_crop);
+ }
+ else
+ {
+ /******************************3D case ****************************/
+ /*Handling output*/
+ B = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(3, dims, mxSINGLE_CLASS, mxREAL));
+ /*allocating memory for the padded arrays */
+ Ap = (float*)mxGetPr(mxCreateNumericArray(3, N_dims, mxSINGLE_CLASS, mxREAL));
+ Bp = (float*)mxGetPr(mxCreateNumericArray(3, N_dims, mxSINGLE_CLASS, mxREAL));
+ /**************************************************************************/
+
+ /*Perform padding of image A to the size of [newsizeX * newsizeY * newsizeZ] */
+ switchpad_crop = 0; /*padding*/
+ pad_crop(A, Ap, M, N, Z, newsizeY, newsizeX, newsizeZ, padXY, switchpad_crop);
+
+ /* Do PB regularization with the padded array */
+ PB_FUNC3D(Ap, Bp, newsizeY, newsizeX, newsizeZ, padXY, SearchW, SimilW, (float)h, (float)lambda);
+
+ switchpad_crop = 1; /*cropping*/
+ pad_crop(Bp, B, M, N, Z, newsizeY, newsizeX, newsizeZ, padXY, switchpad_crop);
+ } /*end else ndims*/
+}
+
+/*2D version*/
+float PB_FUNC2D(float *A, float *B, int dimX, int dimY, int padXY, int SearchW, int SimilW, float h, float lambda)
+{
+ int i, j, i_n, j_n, i_m, j_m, i_p, j_p, i_l, j_l, i1, j1, i2, j2, i3, j3, i5,j5, count, SimilW_full;
+ float *Eucl_Vec, h2, denh2, normsum, Weight, Weight_norm, value, denom, WeightGlob, t1;
+
+ /*SearchW_full = 2*SearchW + 1; */ /* the full searching window size */
+ SimilW_full = 2*SimilW + 1; /* the full similarity window size */
+ h2 = h*h;
+ denh2 = 1/(2*h2);
+
+ /*Gaussian kernel */
+ Eucl_Vec = (float*) calloc (SimilW_full*SimilW_full,sizeof(float));
+ count = 0;
+ for(i_n=-SimilW; i_n<=SimilW; i_n++) {
+ for(j_n=-SimilW; j_n<=SimilW; j_n++) {
+ t1 = pow(((float)i_n), 2) + pow(((float)j_n), 2);
+ Eucl_Vec[count] = exp(-(t1)/(2*SimilW*SimilW));
+ count = count + 1;
+ }} /*main neighb loop */
+
+ /*The NLM code starts here*/
+ /* setting OMP here */
+ #pragma omp parallel for shared (A, B, dimX, dimY, Eucl_Vec, lambda, denh2) private(denom, i, j, WeightGlob, count, i1, j1, i2, j2, i3, j3, i5, j5, Weight_norm, normsum, i_m, j_m, i_n, j_n, i_l, j_l, i_p, j_p, Weight, value)
+
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ if (((i >= padXY) && (i < dimX-padXY)) && ((j >= padXY) && (j < dimY-padXY))) {
+
+ /* Massive Search window loop */
+ Weight_norm = 0; value = 0.0;
+ for(i_m=-SearchW; i_m<=SearchW; i_m++) {
+ for(j_m=-SearchW; j_m<=SearchW; j_m++) {
+ /*checking boundaries*/
+ i1 = i+i_m; j1 = j+j_m;
+
+ WeightGlob = 0.0;
+ /* if inside the searching window */
+ for(i_l=-SimilW; i_l<=SimilW; i_l++) {
+ for(j_l=-SimilW; j_l<=SimilW; j_l++) {
+ i2 = i1+i_l; j2 = j1+j_l;
+
+ i3 = i+i_l; j3 = j+j_l; /*coordinates of the inner patch loop */
+
+ count = 0; normsum = 0.0;
+ for(i_p=-SimilW; i_p<=SimilW; i_p++) {
+ for(j_p=-SimilW; j_p<=SimilW; j_p++) {
+ i5 = i2 + i_p; j5 = j2 + j_p;
+ normsum = normsum + Eucl_Vec[count]*pow(A[(i3+i_p)*dimY+(j3+j_p)]-A[i5*dimY+j5], 2);
+ count = count + 1;
+ }}
+ if (normsum != 0) Weight = (exp(-normsum*denh2));
+ else Weight = 0.0;
+ WeightGlob += Weight;
+ }}
+
+ value += A[i1*dimY+j1]*WeightGlob;
+ Weight_norm += WeightGlob;
+ }} /*search window loop end*/
+
+ /* the final loop to average all values in searching window with weights */
+ denom = 1 + lambda*Weight_norm;
+ B[i*dimY+j] = (A[i*dimY+j] + lambda*value)/denom;
+ }
+ }} /*main loop*/
+ return (*B);
+ free(Eucl_Vec);
+}
+
+/*3D version*/
+ float PB_FUNC3D(float *A, float *B, int dimX, int dimY, int dimZ, int padXY, int SearchW, int SimilW, float h, float lambda)
+ {
+ int SimilW_full, count, i, j, k, i_n, j_n, k_n, i_m, j_m, k_m, i_p, j_p, k_p, i_l, j_l, k_l, i1, j1, k1, i2, j2, k2, i3, j3, k3, i5, j5, k5;
+ float *Eucl_Vec, h2, denh2, normsum, Weight, Weight_norm, value, denom, WeightGlob;
+
+ /*SearchW_full = 2*SearchW + 1; */ /* the full searching window size */
+ SimilW_full = 2*SimilW + 1; /* the full similarity window size */
+ h2 = h*h;
+ denh2 = 1/(2*h2);
+
+ /*Gaussian kernel */
+ Eucl_Vec = (float*) calloc (SimilW_full*SimilW_full*SimilW_full,sizeof(float));
+ count = 0;
+ for(i_n=-SimilW; i_n<=SimilW; i_n++) {
+ for(j_n=-SimilW; j_n<=SimilW; j_n++) {
+ for(k_n=-SimilW; k_n<=SimilW; k_n++) {
+ Eucl_Vec[count] = exp(-(pow((float)i_n, 2) + pow((float)j_n, 2) + pow((float)k_n, 2))/(2*SimilW*SimilW*SimilW));
+ count = count + 1;
+ }}} /*main neighb loop */
+
+ /*The NLM code starts here*/
+ /* setting OMP here */
+ #pragma omp parallel for shared (A, B, dimX, dimY, dimZ, Eucl_Vec, lambda, denh2) private(denom, i, j, k, WeightGlob,count, i1, j1, k1, i2, j2, k2, i3, j3, k3, i5, j5, k5, Weight_norm, normsum, i_m, j_m, k_m, i_n, j_n, k_n, i_l, j_l, k_l, i_p, j_p, k_p, Weight, value)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ for(k=0; k<dimZ; k++) {
+ if (((i >= padXY) && (i < dimX-padXY)) && ((j >= padXY) && (j < dimY-padXY)) && ((k >= padXY) && (k < dimZ-padXY))) {
+ /* take all elements around the pixel of interest */
+ /* Massive Search window loop */
+ Weight_norm = 0; value = 0.0;
+ for(i_m=-SearchW; i_m<=SearchW; i_m++) {
+ for(j_m=-SearchW; j_m<=SearchW; j_m++) {
+ for(k_m=-SearchW; k_m<=SearchW; k_m++) {
+ /*checking boundaries*/
+ i1 = i+i_m; j1 = j+j_m; k1 = k+k_m;
+
+ WeightGlob = 0.0;
+ /* if inside the searching window */
+ for(i_l=-SimilW; i_l<=SimilW; i_l++) {
+ for(j_l=-SimilW; j_l<=SimilW; j_l++) {
+ for(k_l=-SimilW; k_l<=SimilW; k_l++) {
+ i2 = i1+i_l; j2 = j1+j_l; k2 = k1+k_l;
+
+ i3 = i+i_l; j3 = j+j_l; k3 = k+k_l; /*coordinates of the inner patch loop */
+
+ count = 0; normsum = 0.0;
+ for(i_p=-SimilW; i_p<=SimilW; i_p++) {
+ for(j_p=-SimilW; j_p<=SimilW; j_p++) {
+ for(k_p=-SimilW; k_p<=SimilW; k_p++) {
+ i5 = i2 + i_p; j5 = j2 + j_p; k5 = k2 + k_p;
+ normsum = normsum + Eucl_Vec[count]*pow(A[(dimX*dimY)*(k3+k_p)+(i3+i_p)*dimY+(j3+j_p)]-A[(dimX*dimY)*k5 + i5*dimY+j5], 2);
+ count = count + 1;
+ }}}
+ if (normsum != 0) Weight = (exp(-normsum*denh2));
+ else Weight = 0.0;
+ WeightGlob += Weight;
+ }}}
+ value += A[(dimX*dimY)*k1 + i1*dimY+j1]*WeightGlob;
+ Weight_norm += WeightGlob;
+
+ }}} /*search window loop end*/
+
+ /* the final loop to average all values in searching window with weights */
+ denom = 1 + lambda*Weight_norm;
+ B[(dimX*dimY)*k + i*dimY+j] = (A[(dimX*dimY)*k + i*dimY+j] + lambda*value)/denom;
+ }
+ }}} /*main loop*/
+ free(Eucl_Vec);
+ return *B;
+}
+
+float pad_crop(float *A, float *Ap, int OldSizeX, int OldSizeY, int OldSizeZ, int NewSizeX, int NewSizeY, int NewSizeZ, int padXY, int switchpad_crop)
+{
+ /* padding-cropping function */
+ int i,j,k;
+ if (NewSizeZ > 1) {
+ for (i=0; i < NewSizeX; i++) {
+ for (j=0; j < NewSizeY; j++) {
+ for (k=0; k < NewSizeZ; k++) {
+ if (((i >= padXY) && (i < NewSizeX-padXY)) && ((j >= padXY) && (j < NewSizeY-padXY)) && ((k >= padXY) && (k < NewSizeZ-padXY))) {
+ if (switchpad_crop == 0) Ap[NewSizeX*NewSizeY*k + i*NewSizeY+j] = A[OldSizeX*OldSizeY*(k - padXY) + (i-padXY)*(OldSizeY)+(j-padXY)];
+ else Ap[OldSizeX*OldSizeY*(k - padXY) + (i-padXY)*(OldSizeY)+(j-padXY)] = A[NewSizeX*NewSizeY*k + i*NewSizeY+j];
+ }
+ }}}
+ }
+ else {
+ for (i=0; i < NewSizeX; i++) {
+ for (j=0; j < NewSizeY; j++) {
+ if (((i >= padXY) && (i < NewSizeX-padXY)) && ((j >= padXY) && (j < NewSizeY-padXY))) {
+ if (switchpad_crop == 0) Ap[i*NewSizeY+j] = A[(i-padXY)*(OldSizeY)+(j-padXY)];
+ else Ap[(i-padXY)*(OldSizeY)+(j-padXY)] = A[i*NewSizeY+j];
+ }
+ }}
+ }
+ return *Ap;
+}
\ No newline at end of file
diff --git a/main_func/regularizers_CPU/SplitBregman_TV.c b/main_func/regularizers_CPU/SplitBregman_TV.c
new file mode 100644
index 0000000..f143aa6
--- /dev/null
+++ b/main_func/regularizers_CPU/SplitBregman_TV.c
@@ -0,0 +1,399 @@
+#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 [OPTIONAL parameter]
+ * 4. eplsilon - tolerance constant [OPTIONAL parameter]
+ * 5. TV-type: 'iso' or 'l1' [OPTIONAL parameter]
+ *
+ * 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_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_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(
+ 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, *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]);
+
+ /*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 = 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*mu;
+ 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);
+
+ /*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;
+ 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);
+
+ /*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);
+
+ /* 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_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, 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) - 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_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,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;
+
+ 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_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,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++) {
+ 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++) {
+ 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/regularizers_CPU/TGV_PD.c b/main_func/regularizers_CPU/TGV_PD.c
new file mode 100644
index 0000000..41f8615
--- /dev/null
+++ b/main_func/regularizers_CPU/TGV_PD.c
@@ -0,0 +1,353 @@
+#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 Primal-Dual denoising method for
+ * Total Generilized Variation (TGV)-L2 model (2D case only)
+ *
+ * Input Parameters:
+ * 1. Noisy image/volume (2D)
+ * 2. lambda - regularization parameter
+ * 3. parameter to control first-order term (alpha1)
+ * 4. parameter to control the second-order term (alpha0)
+ * 5. Number of CP iterations
+ *
+ * Output:
+ * Filtered/regularized image
+ *
+ * Example:
+ * figure;
+ * Im = double(imread('lena_gray_256.tif'))/255; % loading image
+ * u0 = Im + .03*randn(size(Im)); % adding noise
+ * tic; u = PrimalDual_TGV(single(u0), 0.02, 1.3, 1, 550); toc;
+ *
+ * to compile with OMP support: mex TGV_PD.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp"
+ * References:
+ * K. Bredies "Total Generalized Variation"
+ *
+ * 28.11.16/Harwell
+ */
+
+/* 2D functions */
+float DualP_2D(float *U, float *V1, float *V2, float *P1, float *P2, int dimX, int dimY, int dimZ, float sigma);
+float ProjP_2D(float *P1, float *P2, int dimX, int dimY, int dimZ, float alpha1);
+float DualQ_2D(float *V1, float *V2, float *Q1, float *Q2, float *Q3, int dimX, int dimY, int dimZ, float sigma);
+float ProjQ_2D(float *Q1, float *Q2, float *Q3, int dimX, int dimY, int dimZ, float alpha0);
+float DivProjP_2D(float *U, float *A, float *P1, float *P2, int dimX, int dimY, int dimZ, float lambda, float tau);
+float UpdV_2D(float *V1, float *V2, float *P1, float *P2, float *Q1, float *Q2, float *Q3, int dimX, int dimY, int dimZ, float tau);
+/*3D functions*/
+float DualP_3D(float *U, float *V1, float *V2, float *V3, float *P1, float *P2, float *P3, int dimX, int dimY, int dimZ, float sigma);
+
+float newU(float *U, float *U_old, 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;
+ const int *dim_array;
+ float *A, *U, *U_old, *P1, *P2, *P3, *Q1, *Q2, *Q3, *Q4, *Q5, *Q6, *Q7, *Q8, *Q9, *V1, *V1_old, *V2, *V2_old, *V3, *V3_old, lambda, L2, tau, sigma, alpha1, alpha0;
+
+ number_of_dims = mxGetNumberOfDimensions(prhs[0]);
+ dim_array = mxGetDimensions(prhs[0]);
+
+ /*Handling Matlab input data*/
+ A = (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*/
+ alpha1 = (float) mxGetScalar(prhs[2]); /*first-order term*/
+ alpha0 = (float) mxGetScalar(prhs[3]); /*second-order term*/
+ iter = (int) mxGetScalar(prhs[4]); /*iterations number*/
+ if(nrhs != 5) mexErrMsgTxt("Five input parameters is reqired: Image(2D/3D), Regularization parameter, alpha1, alpha0, Iterations");
+
+ /*Handling Matlab output data*/
+ dimX = dim_array[0]; dimY = dim_array[1];
+
+ if (number_of_dims == 2) {
+ /*2D case*/
+ dimZ = 1;
+ U = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+
+ /*dual variables*/
+ P1 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ P2 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+
+ Q1 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ Q2 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ Q3 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+
+ U_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+
+ V1 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ V1_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ V2 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL));
+ V2_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); }
+ else if (number_of_dims == 3) {
+ mexErrMsgTxt("The input data should be 2D");
+ /*3D case*/
+// dimZ = dim_array[2];
+// U = (float*)mxGetPr(plhs[0] = 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));
+//
+// Q1 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+// Q2 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+// Q3 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+// Q4 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+// Q5 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+// Q6 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+// Q7 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+// Q8 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+// Q9 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+//
+// U_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+//
+// V1 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+// V1_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+// V2 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+// V2_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+// V3 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+// V3_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL));
+ }
+ else {mexErrMsgTxt("The input data should be 2D");}
+
+
+ /*printf("%i \n", i);*/
+ L2 = 12.0; /*Lipshitz constant*/
+ tau = 1.0/pow(L2,0.5);
+ sigma = 1.0/pow(L2,0.5);
+
+ /*Copy A to U*/
+ copyIm(A, U, dimX, dimY, dimZ);
+
+ if (number_of_dims == 2) {
+ /* Here primal-dual iterations begin for 2D */
+ for(ll = 0; ll < iter; ll++) {
+
+ /* Calculate Dual Variable P */
+ DualP_2D(U, V1, V2, P1, P2, dimX, dimY, dimZ, sigma);
+
+ /*Projection onto convex set for P*/
+ ProjP_2D(P1, P2, dimX, dimY, dimZ, alpha1);
+
+ /* Calculate Dual Variable Q */
+ DualQ_2D(V1, V2, Q1, Q2, Q3, dimX, dimY, dimZ, sigma);
+
+ /*Projection onto convex set for Q*/
+ ProjQ_2D(Q1, Q2, Q3, dimX, dimY, dimZ, alpha0);
+
+ /*saving U into U_old*/
+ copyIm(U, U_old, dimX, dimY, dimZ);
+
+ /*adjoint operation -> divergence and projection of P*/
+ DivProjP_2D(U, A, P1, P2, dimX, dimY, dimZ, lambda, tau);
+
+ /*get updated solution U*/
+ newU(U, U_old, dimX, dimY, dimZ);
+
+ /*saving V into V_old*/
+ copyIm(V1, V1_old, dimX, dimY, dimZ);
+ copyIm(V2, V2_old, dimX, dimY, dimZ);
+
+ /* upd V*/
+ UpdV_2D(V1, V2, P1, P2, Q1, Q2, Q3, dimX, dimY, dimZ, tau);
+
+ /*get new V*/
+ newU(V1, V1_old, dimX, dimY, dimZ);
+ newU(V2, V2_old, dimX, dimY, dimZ);
+ } /*end of iterations*/
+ }
+
+// /*3D version*/
+// if (number_of_dims == 3) {
+// /* Here primal-dual iterations begin for 3D */
+// for(ll = 0; ll < iter; ll++) {
+//
+// /* Calculate Dual Variable P */
+// DualP_3D(U, V1, V2, V3, P1, P2, P3, dimX, dimY, dimZ, sigma);
+//
+// /*Projection onto convex set for P*/
+// ProjP_3D(P1, P2, P3, dimX, dimY, dimZ, alpha1);
+//
+// /* Calculate Dual Variable Q */
+// DualQ_3D(V1, V2, V2, Q1, Q2, Q3, Q4, Q5, Q6, Q7, Q8, Q9, dimX, dimY, dimZ, sigma);
+//
+// } /*end of iterations*/
+// }
+}
+
+/*Calculating dual variable P (using forward differences)*/
+float DualP_2D(float *U, float *V1, float *V2, float *P1, float *P2, int dimX, int dimY, int dimZ, float sigma)
+{
+ int i,j;
+#pragma omp parallel for shared(U,V1,V2,P1,P2) private(i,j)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ /* symmetric boundary conditions (Neuman) */
+ if (i == dimX-1) P1[i*dimY + (j)] = P1[i*dimY + (j)] + sigma*((U[(i-1)*dimY + (j)] - U[i*dimY + (j)]) - V1[i*dimY + (j)]);
+ else P1[i*dimY + (j)] = P1[i*dimY + (j)] + sigma*((U[(i + 1)*dimY + (j)] - U[i*dimY + (j)]) - V1[i*dimY + (j)]);
+ if (j == dimY-1) P2[i*dimY + (j)] = P2[i*dimY + (j)] + sigma*((U[(i)*dimY + (j-1)] - U[i*dimY + (j)]) - V2[i*dimY + (j)]);
+ else P2[i*dimY + (j)] = P2[i*dimY + (j)] + sigma*((U[(i)*dimY + (j+1)] - U[i*dimY + (j)]) - V2[i*dimY + (j)]);
+ }}
+ return 1;
+}
+/*Projection onto convex set for P*/
+float ProjP_2D(float *P1, float *P2, int dimX, int dimY, int dimZ, float alpha1)
+{
+ float grad_magn;
+ int i,j;
+#pragma omp parallel for shared(P1,P2) private(i,j,grad_magn)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ grad_magn = sqrt(pow(P1[i*dimY + (j)],2) + pow(P2[i*dimY + (j)],2));
+ grad_magn = grad_magn/alpha1;
+ if (grad_magn > 1.0) {
+ P1[i*dimY + (j)] = P1[i*dimY + (j)]/grad_magn;
+ P2[i*dimY + (j)] = P2[i*dimY + (j)]/grad_magn;
+ }
+ }}
+ return 1;
+}
+/*Calculating dual variable Q (using forward differences)*/
+float DualQ_2D(float *V1, float *V2, float *Q1, float *Q2, float *Q3, int dimX, int dimY, int dimZ, float sigma)
+{
+ int i,j;
+ float q1, q2, q11, q22;
+#pragma omp parallel for shared(Q1,Q2,Q3,V1,V2) private(i,j,q1,q2,q11,q22)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ /* symmetric boundary conditions (Neuman) */
+ if (i == dimX-1)
+ { q1 = (V1[(i-1)*dimY + (j)] - V1[i*dimY + (j)]);
+ q11 = (V2[(i-1)*dimY + (j)] - V2[i*dimY + (j)]);
+ }
+ else {
+ q1 = (V1[(i+1)*dimY + (j)] - V1[i*dimY + (j)]);
+ q11 = (V2[(i+1)*dimY + (j)] - V2[i*dimY + (j)]);
+ }
+ if (j == dimY-1) {
+ q2 = (V2[(i)*dimY + (j-1)] - V2[i*dimY + (j)]);
+ q22 = (V1[(i)*dimY + (j-1)] - V1[i*dimY + (j)]);
+ }
+ else {
+ q2 = (V2[(i)*dimY + (j+1)] - V2[i*dimY + (j)]);
+ q22 = (V1[(i)*dimY + (j+1)] - V1[i*dimY + (j)]);
+ }
+ Q1[i*dimY + (j)] = Q1[i*dimY + (j)] + sigma*(q1);
+ Q2[i*dimY + (j)] = Q2[i*dimY + (j)] + sigma*(q2);
+ Q3[i*dimY + (j)] = Q3[i*dimY + (j)] + sigma*(0.5f*(q11 + q22));
+ }}
+ return 1;
+}
+
+float ProjQ_2D(float *Q1, float *Q2, float *Q3, int dimX, int dimY, int dimZ, float alpha0)
+{
+ float grad_magn;
+ int i,j;
+#pragma omp parallel for shared(Q1,Q2,Q3) private(i,j,grad_magn)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ grad_magn = sqrt(pow(Q1[i*dimY + (j)],2) + pow(Q2[i*dimY + (j)],2) + 2*pow(Q3[i*dimY + (j)],2));
+ grad_magn = grad_magn/alpha0;
+ if (grad_magn > 1.0) {
+ Q1[i*dimY + (j)] = Q1[i*dimY + (j)]/grad_magn;
+ Q2[i*dimY + (j)] = Q2[i*dimY + (j)]/grad_magn;
+ Q3[i*dimY + (j)] = Q3[i*dimY + (j)]/grad_magn;
+ }
+ }}
+ return 1;
+}
+/* Divergence and projection for P*/
+float DivProjP_2D(float *U, float *A, float *P1, float *P2, int dimX, int dimY, int dimZ, float lambda, float tau)
+{
+ int i,j;
+ float P_v1, P_v2, div;
+#pragma omp parallel for shared(U,A,P1,P2) private(i,j,P_v1,P_v2,div)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ if (i == 0) P_v1 = (P1[i*dimY + (j)]);
+ else P_v1 = (P1[i*dimY + (j)] - P1[(i-1)*dimY + (j)]);
+ if (j == 0) P_v2 = (P2[i*dimY + (j)]);
+ else P_v2 = (P2[i*dimY + (j)] - P2[(i)*dimY + (j-1)]);
+ div = P_v1 + P_v2;
+ U[i*dimY + (j)] = (lambda*(U[i*dimY + (j)] + tau*div) + tau*A[i*dimY + (j)])/(lambda + tau);
+ }}
+ return *U;
+}
+/*get updated solution U*/
+float newU(float *U, float *U_old, int dimX, int dimY, int dimZ)
+{
+ int i;
+#pragma omp parallel for shared(U,U_old) private(i)
+ for(i=0; i<dimX*dimY*dimZ; i++) U[i] = 2*U[i] - U_old[i];
+ return *U;
+}
+
+/*get update for V*/
+float UpdV_2D(float *V1, float *V2, float *P1, float *P2, float *Q1, float *Q2, float *Q3, int dimX, int dimY, int dimZ, float tau)
+{
+ int i,j;
+ float q1, q11, q2, q22, div1, div2;
+#pragma omp parallel for shared(V1,V2,P1,P2,Q1,Q2,Q3) private(i,j, q1, q11, q2, q22, div1, div2)
+ for(i=0; i<dimX; i++) {
+ for(j=0; j<dimY; j++) {
+ /* symmetric boundary conditions (Neuman) */
+ if (i == 0) {
+ q1 = (Q1[i*dimY + (j)]);
+ q11 = (Q3[i*dimY + (j)]);
+ }
+ else {
+ q1 = (Q1[i*dimY + (j)] - Q1[(i-1)*dimY + (j)]);
+ q11 = (Q3[i*dimY + (j)] - Q3[(i-1)*dimY + (j)]);
+ }
+ if (j == 0) {
+ q2 = (Q2[i*dimY + (j)]);
+ q22 = (Q3[i*dimY + (j)]);
+ }
+ else {
+ q2 = (Q2[i*dimY + (j)] - Q2[(i)*dimY + (j-1)]);
+ q22 = (Q3[i*dimY + (j)] - Q3[(i)*dimY + (j-1)]);
+ }
+ div1 = q1 + q22;
+ div2 = q2 + q11;
+ V1[i*dimY + (j)] = V1[i*dimY + (j)] + tau*(P1[i*dimY + (j)] + div1);
+ V2[i*dimY + (j)] = V2[i*dimY + (j)] + tau*(P2[i*dimY + (j)] + div2);
+ }}
+ return 1;
+}
+/* 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 *********************/
+
+/*Calculating dual variable P (using forward differences)*/
+float DualP_3D(float *U, float *V1, float *V2, float *V3, float *P1, float *P2, float *P3, int dimX, int dimY, int dimZ, float sigma)
+{
+ int i,j,k;
+#pragma omp parallel for shared(U,V1,V2,V3,P1,P2,P3) private(i,j,k)
+ 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) P1[dimX*dimY*k + i*dimY + (j)] = P1[dimX*dimY*k + i*dimY + (j)] + sigma*((U[dimX*dimY*k + (i-1)*dimY + (j)] - U[dimX*dimY*k + i*dimY + (j)]) - V1[dimX*dimY*k + i*dimY + (j)]);
+ else P1[dimX*dimY*k + i*dimY + (j)] = P1[dimX*dimY*k + i*dimY + (j)] + sigma*((U[dimX*dimY*k + (i + 1)*dimY + (j)] - U[dimX*dimY*k + i*dimY + (j)]) - V1[dimX*dimY*k + i*dimY + (j)]);
+ if (j == dimY-1) P2[dimX*dimY*k + i*dimY + (j)] = P2[dimX*dimY*k + i*dimY + (j)] + sigma*((U[dimX*dimY*k + (i)*dimY + (j-1)] - U[dimX*dimY*k + i*dimY + (j)]) - V2[dimX*dimY*k + i*dimY + (j)]);
+ else P2[dimX*dimY*k + i*dimY + (j)] = P2[dimX*dimY*k + i*dimY + (j)] + sigma*((U[dimX*dimY*k + (i)*dimY + (j+1)] - U[dimX*dimY*k + i*dimY + (j)]) - V2[dimX*dimY*k + i*dimY + (j)]);
+ if (k == dimZ-1) P3[dimX*dimY*k + i*dimY + (j)] = P3[dimX*dimY*k + i*dimY + (j)] + sigma*((U[dimX*dimY*(k-1) + (i)*dimY + (j)] - U[dimX*dimY*k + i*dimY + (j)]) - V3[dimX*dimY*k + i*dimY + (j)]);
+ else P3[dimX*dimY*k + i*dimY + (j)] = P3[dimX*dimY*k + i*dimY + (j)] + sigma*((U[dimX*dimY*(k+1) + (i)*dimY + (j)] - U[dimX*dimY*k + i*dimY + (j)]) - V3[dimX*dimY*k + i*dimY + (j)]);
+ }}}
+ return 1;
+}
\ No newline at end of file
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