From 5d4464a78d1807565a75c9430cfe5e6857fe9232 Mon Sep 17 00:00:00 2001 From: Daniil Kazantsev 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 -#include -#include -#include -#include -#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 3) { - Obj_func2D(A, D, P1, P2, lambda, dimX, dimY); - funcval = 0.0f; - for(j=0; j 2) { - if (re > re_old) { - Obj_func2D(A, D, P1, P2, lambda, dimX, dimY); - funcval = 0.0f; - for(j=0; j 3) { - Obj_func3D(A, D, P1, P2, P3,lambda, dimX, dimY, dimZ); - funcval = 0.0f; - for(j=0; j 2) { - if (re > re_old) { - Obj_func3D(A, D, P1, P2, P3,lambda, dimX, dimY, dimZ); - funcval = 0.0f; - for(j=0; j 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 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 -#include -#include -#include -#include -#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 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 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= 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= 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 maxval) maxval = U[dimX*dimY*k + i*dimY + j]; - }}} - - if (maxval != 0.0f) { - for(i=0; i= 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= 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 -#include -#include -#include -#include -#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 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 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 +#include +#include +#include +#include +#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 3) { + Obj_func2D(A, D, P1, P2, lambda, dimX, dimY); + funcval = 0.0f; + for(j=0; j 2) { + if (re > re_old) { + Obj_func2D(A, D, P1, P2, lambda, dimX, dimY); + funcval = 0.0f; + for(j=0; j 3) { + Obj_func3D(A, D, P1, P2, P3,lambda, dimX, dimY, dimZ); + funcval = 0.0f; + for(j=0; j 2) { + if (re > re_old) { + Obj_func3D(A, D, P1, P2, P3,lambda, dimX, dimY, dimZ); + funcval = 0.0f; + for(j=0; j 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 +#include +#include +#include +#include +#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 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 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= 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= 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 maxval) maxval = U[dimX*dimY*k + i*dimY + j]; + }}} + + if (maxval != 0.0f) { + for(i=0; i= 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= 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 +#include +#include +#include +#include +#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= 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= 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 +#include +#include +#include +#include +#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 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 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 +#include +#include +#include +#include +#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 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 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