diff options
Diffstat (limited to 'main_func')
| -rw-r--r-- | main_func/FGP_TV.c | 400 | ||||
| -rw-r--r-- | main_func/FISTA_REC.m | 291 | ||||
| -rw-r--r-- | main_func/FISTA_TV.c | 331 | ||||
| -rw-r--r-- | main_func/LLT_model.c | 2 | ||||
| -rw-r--r-- | main_func/SplitBregman_TV.c | 317 | ||||
| -rw-r--r-- | main_func/compile_mex.m | 4 | ||||
| -rw-r--r-- | main_func/studentst.m | 94 |
7 files changed, 785 insertions, 654 deletions
diff --git a/main_func/FGP_TV.c b/main_func/FGP_TV.c new file mode 100644 index 0000000..1a1fd13 --- /dev/null +++ b/main_func/FGP_TV.c @@ -0,0 +1,400 @@ +#include "mex.h" +#include <matrix.h> +#include <math.h> +#include <stdlib.h> +#include <memory.h> +#include <stdio.h> +#include "omp.h" + +/* C-OMP implementation of FGP-TV [1] denoising/regularization model (2D/3D case) + * + * Input Parameters: + * 1. Noisy image/volume [REQUIRED] + * 2. lambda - regularization parameter [REQUIRED] + * 3. Number of iterations [OPTIONAL parameter] + * 4. eplsilon: tolerance constant [OPTIONAL parameter] + * 5. TV-type: 'iso' or 'l1' [OPTIONAL parameter] + * + * Output: + * [1] Filtered/regularized image + * [2] last function value + * + * Example of image denoising: + * figure; + * Im = double(imread('lena_gray_256.tif'))/255; % loading image + * u0 = Im + .05*randn(size(Im)); % adding noise + * u = FGP_TV(single(u0), 0.05, 100, 1e-04); + * + * to compile with OMP support: mex FGP_TV.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp" + * This function is based on the Matlab's code and paper by + * [1] Amir Beck and Marc Teboulle, "Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems" + * + * D. Kazantsev, 2016-17 + * + */ + +float copyIm(float *A, float *B, int dimX, int dimY, int dimZ); +float Obj_func2D(float *A, float *D, float *R1, float *R2, float lambda, int dimX, int dimY); +float Grad_func2D(float *P1, float *P2, float *D, float *R1, float *R2, float lambda, int dimX, int dimY); +float Proj_func2D(float *P1, float *P2, int methTV, int dimX, int dimY); +float Rupd_func2D(float *P1, float *P1_old, float *P2, float *P2_old, float *R1, float *R2, float tkp1, float tk, int dimX, int dimY); + +float Obj_func3D(float *A, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ); +float Grad_func3D(float *P1, float *P2, float *P3, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ); +float Proj_func3D(float *P1, float *P2, float *P3, int dimX, int dimY, int dimZ); +float Rupd_func3D(float *P1, float *P1_old, float *P2, float *P2_old, float *P3, float *P3_old, float *R1, float *R2, float *R3, float tkp1, float tk, int dimX, int dimY, int dimZ); + + +void mexFunction( + int nlhs, mxArray *plhs[], + int nrhs, const mxArray *prhs[]) + +{ + int number_of_dims, iter, dimX, dimY, dimZ, ll, j, count, methTV; + const int *dim_array; + float *A, *D=NULL, *D_old=NULL, *P1=NULL, *P2=NULL, *P3=NULL, *P1_old=NULL, *P2_old=NULL, *P3_old=NULL, *R1=NULL, *R2=NULL, *R3=NULL, lambda, tk, tkp1, re, re1, re_old, epsil, funcval; + + number_of_dims = mxGetNumberOfDimensions(prhs[0]); + dim_array = mxGetDimensions(prhs[0]); + + /*Handling Matlab input data*/ + if ((nrhs < 2) || (nrhs > 5)) mexErrMsgTxt("At least 2 parameters is required: Image(2D/3D), Regularization parameter. The full list of parameters: Image(2D/3D), Regularization parameter, iterations number, tolerance, penalty type ('iso' or 'l1')"); + + A = (float *) mxGetData(prhs[0]); /*noisy image (2D/3D) */ + lambda = (float) mxGetScalar(prhs[1]); /* regularization parameter */ + iter = 50; /* default iterations number */ + epsil = 0.001; /* default tolerance constant */ + methTV = 0; /* default isotropic TV penalty */ + + if ((nrhs == 3) || (nrhs == 4) || (nrhs == 5)) iter = (int) mxGetScalar(prhs[2]); /* iterations number */ + if ((nrhs == 4) || (nrhs == 5)) epsil = (float) mxGetScalar(prhs[3]); /* tolerance constant */ + if (nrhs == 5) { + char *penalty_type; + penalty_type = mxArrayToString(prhs[4]); /* choosing TV penalty: 'iso' or 'l1', 'iso' is the default */ + if ((strcmp(penalty_type, "l1") != 0) && (strcmp(penalty_type, "iso") != 0)) mexErrMsgTxt("Choose TV type: 'iso' or 'l1',"); + if (strcmp(penalty_type, "l1") == 0) methTV = 1; /* enable 'l1' penalty */ + mxFree(penalty_type); + } + /*output function value (last iteration) */ + funcval = 0.0f; + plhs[1] = mxCreateNumericMatrix(1, 1, mxSINGLE_CLASS, mxREAL); + float *funcvalA = (float *) mxGetData(plhs[1]); + + if (mxGetClassID(prhs[0]) != mxSINGLE_CLASS) {mexErrMsgTxt("The input image must be in a single precision"); } + + /*Handling Matlab output data*/ + dimX = dim_array[0]; dimY = dim_array[1]; dimZ = dim_array[2]; + + tk = 1.0f; + tkp1=1.0f; + count = 1; + re_old = 0.0f; + + if (number_of_dims == 2) { + dimZ = 1; /*2D case*/ + D = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); + D_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); + P1 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); + P2 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); + P1_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); + P2_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); + R1 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); + R2 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); + + /* begin iterations */ + for(ll=0; ll<iter; ll++) { + + /* computing the gradient of the objective function */ + Obj_func2D(A, D, R1, R2, lambda, dimX, dimY); + + /*Taking a step towards minus of the gradient*/ + Grad_func2D(P1, P2, D, R1, R2, lambda, dimX, dimY); + + /* projection step */ + Proj_func2D(P1, P2, methTV, dimX, dimY); + + /*updating R and t*/ + tkp1 = (1.0f + sqrt(1.0f + 4.0f*tk*tk))*0.5f; + Rupd_func2D(P1, P1_old, P2, P2_old, R1, R2, tkp1, tk, dimX, dimY); + + /* calculate norm */ + re = 0.0f; re1 = 0.0f; + for(j=0; j<dimX*dimY*dimZ; j++) + { + re += pow(D[j] - D_old[j],2); + re1 += pow(D[j],2); + } + re = sqrt(re)/sqrt(re1); + if (re < epsil) count++; + if (count > 3) { + Obj_func2D(A, D, P1, P2, lambda, dimX, dimY); + funcval = 0.0f; + for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2); + funcvalA[0] = sqrt(funcval); + break; } + + /* check that the residual norm is decreasing */ + if (ll > 2) { + if (re > re_old) { + Obj_func2D(A, D, P1, P2, lambda, dimX, dimY); + funcval = 0.0f; + for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2); + funcvalA[0] = sqrt(funcval); + break; }} + re_old = re; + /*printf("%f %i %i \n", re, ll, count); */ + + /*storing old values*/ + copyIm(D, D_old, dimX, dimY, dimZ); + copyIm(P1, P1_old, dimX, dimY, dimZ); + copyIm(P2, P2_old, dimX, dimY, dimZ); + tk = tkp1; + + /* calculating the objective function value */ + if (ll == (iter-1)) { + Obj_func2D(A, D, P1, P2, lambda, dimX, dimY); + funcval = 0.0f; + for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2); + funcvalA[0] = sqrt(funcval); + } + } + printf("FGP-TV iterations stopped at iteration %i with the function value %f \n", ll, funcvalA[0]); + } + if (number_of_dims == 3) { + D = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); + D_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); + P1 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); + P2 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); + P3 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); + P1_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); + P2_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); + P3_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); + R1 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); + R2 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); + R3 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); + + /* begin iterations */ + for(ll=0; ll<iter; ll++) { + + /* computing the gradient of the objective function */ + Obj_func3D(A, D, R1, R2, R3,lambda, dimX, dimY, dimZ); + + /*Taking a step towards minus of the gradient*/ + Grad_func3D(P1, P2, P3, D, R1, R2, R3, lambda, dimX, dimY, dimZ); + + /* projection step */ + Proj_func3D(P1, P2, P3, dimX, dimY, dimZ); + + /*updating R and t*/ + tkp1 = (1.0f + sqrt(1.0f + 4.0f*tk*tk))*0.5f; + Rupd_func3D(P1, P1_old, P2, P2_old, P3, P3_old, R1, R2, R3, tkp1, tk, dimX, dimY, dimZ); + + /* calculate norm - stopping rules*/ + re = 0.0f; re1 = 0.0f; + for(j=0; j<dimX*dimY*dimZ; j++) + { + re += pow(D[j] - D_old[j],2); + re1 += pow(D[j],2); + } + re = sqrt(re)/sqrt(re1); + /* stop if the norm residual is less than the tolerance EPS */ + if (re < epsil) count++; + if (count > 3) { + Obj_func3D(A, D, P1, P2, P3,lambda, dimX, dimY, dimZ); + funcval = 0.0f; + for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2); + funcvalA[0] = sqrt(funcval); + break;} + + /* check that the residual norm is decreasing */ + if (ll > 2) { + if (re > re_old) { + Obj_func3D(A, D, P1, P2, P3,lambda, dimX, dimY, dimZ); + funcval = 0.0f; + for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2); + funcvalA[0] = sqrt(funcval); + break; }} + + re_old = re; + /*printf("%f %i %i \n", re, ll, count); */ + + /*storing old values*/ + copyIm(D, D_old, dimX, dimY, dimZ); + copyIm(P1, P1_old, dimX, dimY, dimZ); + copyIm(P2, P2_old, dimX, dimY, dimZ); + copyIm(P3, P3_old, dimX, dimY, dimZ); + tk = tkp1; + + if (ll == (iter-1)) { + Obj_func3D(A, D, P1, P2, P3,lambda, dimX, dimY, dimZ); + funcval = 0.0f; + for(j=0; j<dimX*dimY*dimZ; j++) funcval += pow(D[j],2); + funcvalA[0] = sqrt(funcval); + } + + } + printf("FGP-TV iterations stopped at iteration %i with the function value %f \n", ll, funcvalA[0]); + } +} + +/* 2D-case related Functions */ +/*****************************************************************/ +float Obj_func2D(float *A, float *D, float *R1, float *R2, float lambda, int dimX, int dimY) +{ + float val1, val2; + int i,j; +#pragma omp parallel for shared(A,D,R1,R2) private(i,j,val1,val2) + for(i=0; i<dimX; i++) { + for(j=0; j<dimY; j++) { + /* boundary conditions */ + if (i == 0) {val1 = 0.0f;} else {val1 = R1[(i-1)*dimY + (j)];} + if (j == 0) {val2 = 0.0f;} else {val2 = R2[(i)*dimY + (j-1)];} + D[(i)*dimY + (j)] = A[(i)*dimY + (j)] - lambda*(R1[(i)*dimY + (j)] + R2[(i)*dimY + (j)] - val1 - val2); + }} + return *D; +} +float Grad_func2D(float *P1, float *P2, float *D, float *R1, float *R2, float lambda, int dimX, int dimY) +{ + float val1, val2, multip; + int i,j; + multip = (1.0f/(8.0f*lambda)); +#pragma omp parallel for shared(P1,P2,D,R1,R2,multip) private(i,j,val1,val2) + for(i=0; i<dimX; i++) { + for(j=0; j<dimY; j++) { + /* boundary conditions */ + if (i == dimX-1) val1 = 0.0f; else val1 = D[(i)*dimY + (j)] - D[(i+1)*dimY + (j)]; + if (j == dimY-1) val2 = 0.0f; else val2 = D[(i)*dimY + (j)] - D[(i)*dimY + (j+1)]; + P1[(i)*dimY + (j)] = R1[(i)*dimY + (j)] + multip*val1; + P2[(i)*dimY + (j)] = R2[(i)*dimY + (j)] + multip*val2; + }} + return 1; +} +float Proj_func2D(float *P1, float *P2, int methTV, int dimX, int dimY) +{ + float val1, val2, denom; + int i,j; + if (methTV == 0) { + /* isotropic TV*/ +#pragma omp parallel for shared(P1,P2) private(i,j,denom) + for(i=0; i<dimX; i++) { + for(j=0; j<dimY; j++) { + denom = pow(P1[(i)*dimY + (j)],2) + pow(P2[(i)*dimY + (j)],2); + if (denom > 1) { + P1[(i)*dimY + (j)] = P1[(i)*dimY + (j)]/sqrt(denom); + P2[(i)*dimY + (j)] = P2[(i)*dimY + (j)]/sqrt(denom); + } + }} + } + else { + /* anisotropic TV*/ +#pragma omp parallel for shared(P1,P2) private(i,j,val1,val2) + for(i=0; i<dimX; i++) { + for(j=0; j<dimY; j++) { + val1 = fabs(P1[(i)*dimY + (j)]); + val2 = fabs(P2[(i)*dimY + (j)]); + if (val1 < 1.0f) {val1 = 1.0f;} + if (val2 < 1.0f) {val2 = 1.0f;} + P1[(i)*dimY + (j)] = P1[(i)*dimY + (j)]/val1; + P2[(i)*dimY + (j)] = P2[(i)*dimY + (j)]/val2; + }} + } + return 1; +} +float Rupd_func2D(float *P1, float *P1_old, float *P2, float *P2_old, float *R1, float *R2, float tkp1, float tk, int dimX, int dimY) +{ + int i,j; + float multip; + multip = ((tk-1.0f)/tkp1); +#pragma omp parallel for shared(P1,P2,P1_old,P2_old,R1,R2,multip) private(i,j) + for(i=0; i<dimX; i++) { + for(j=0; j<dimY; j++) { + R1[(i)*dimY + (j)] = P1[(i)*dimY + (j)] + multip*(P1[(i)*dimY + (j)] - P1_old[(i)*dimY + (j)]); + R2[(i)*dimY + (j)] = P2[(i)*dimY + (j)] + multip*(P2[(i)*dimY + (j)] - P2_old[(i)*dimY + (j)]); + }} + return 1; +} + +/* 3D-case related Functions */ +/*****************************************************************/ +float Obj_func3D(float *A, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ) +{ + float val1, val2, val3; + int i,j,k; +#pragma omp parallel for shared(A,D,R1,R2,R3) private(i,j,k,val1,val2,val3) + for(i=0; i<dimX; i++) { + for(j=0; j<dimY; j++) { + for(k=0; k<dimZ; k++) { + /* boundary conditions */ + if (i == 0) {val1 = 0.0f;} else {val1 = R1[(dimX*dimY)*k + (i-1)*dimY + (j)];} + if (j == 0) {val2 = 0.0f;} else {val2 = R2[(dimX*dimY)*k + (i)*dimY + (j-1)];} + if (k == 0) {val3 = 0.0f;} else {val3 = R3[(dimX*dimY)*(k-1) + (i)*dimY + (j)];} + D[(dimX*dimY)*k + (i)*dimY + (j)] = A[(dimX*dimY)*k + (i)*dimY + (j)] - lambda*(R1[(dimX*dimY)*k + (i)*dimY + (j)] + R2[(dimX*dimY)*k + (i)*dimY + (j)] + R3[(dimX*dimY)*k + (i)*dimY + (j)] - val1 - val2 - val3); + }}} + return *D; +} +float Grad_func3D(float *P1, float *P2, float *P3, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ) +{ + float val1, val2, val3, multip; + int i,j,k; + multip = (1.0f/(8.0f*lambda)); +#pragma omp parallel for shared(P1,P2,P3,D,R1,R2,R3,multip) private(i,j,k,val1,val2,val3) + for(i=0; i<dimX; i++) { + for(j=0; j<dimY; j++) { + for(k=0; k<dimZ; k++) { + /* boundary conditions */ + if (i == dimX-1) val1 = 0.0f; else val1 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*k + (i+1)*dimY + (j)]; + if (j == dimY-1) val2 = 0.0f; else val2 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*k + (i)*dimY + (j+1)]; + if (k == dimZ-1) val3 = 0.0f; else val3 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*(k+1) + (i)*dimY + (j)]; + P1[(dimX*dimY)*k + (i)*dimY + (j)] = R1[(dimX*dimY)*k + (i)*dimY + (j)] + multip*val1; + P2[(dimX*dimY)*k + (i)*dimY + (j)] = R2[(dimX*dimY)*k + (i)*dimY + (j)] + multip*val2; + P3[(dimX*dimY)*k + (i)*dimY + (j)] = R3[(dimX*dimY)*k + (i)*dimY + (j)] + multip*val3; + }}} + return 1; +} +float Proj_func3D(float *P1, float *P2, float *P3, int dimX, int dimY, int dimZ) +{ + float val1, val2, val3; + int i,j,k; +#pragma omp parallel for shared(P1,P2,P3) private(i,j,k,val1,val2,val3) + for(i=0; i<dimX; i++) { + for(j=0; j<dimY; j++) { + for(k=0; k<dimZ; k++) { + val1 = fabs(P1[(dimX*dimY)*k + (i)*dimY + (j)]); + val2 = fabs(P2[(dimX*dimY)*k + (i)*dimY + (j)]); + val3 = fabs(P3[(dimX*dimY)*k + (i)*dimY + (j)]); + if (val1 < 1.0f) {val1 = 1.0f;} + if (val2 < 1.0f) {val2 = 1.0f;} + if (val3 < 1.0f) {val3 = 1.0f;} + + P1[(dimX*dimY)*k + (i)*dimY + (j)] = P1[(dimX*dimY)*k + (i)*dimY + (j)]/val1; + P2[(dimX*dimY)*k + (i)*dimY + (j)] = P2[(dimX*dimY)*k + (i)*dimY + (j)]/val2; + P3[(dimX*dimY)*k + (i)*dimY + (j)] = P3[(dimX*dimY)*k + (i)*dimY + (j)]/val3; + }}} + return 1; +} +float Rupd_func3D(float *P1, float *P1_old, float *P2, float *P2_old, float *P3, float *P3_old, float *R1, float *R2, float *R3, float tkp1, float tk, int dimX, int dimY, int dimZ) +{ + int i,j,k; + float multip; + multip = ((tk-1.0f)/tkp1); +#pragma omp parallel for shared(P1,P2,P3,P1_old,P2_old,P3_old,R1,R2,R3,multip) private(i,j,k) + for(i=0; i<dimX; i++) { + for(j=0; j<dimY; j++) { + for(k=0; k<dimZ; k++) { + R1[(dimX*dimY)*k + (i)*dimY + (j)] = P1[(dimX*dimY)*k + (i)*dimY + (j)] + multip*(P1[(dimX*dimY)*k + (i)*dimY + (j)] - P1_old[(dimX*dimY)*k + (i)*dimY + (j)]); + R2[(dimX*dimY)*k + (i)*dimY + (j)] = P2[(dimX*dimY)*k + (i)*dimY + (j)] + multip*(P2[(dimX*dimY)*k + (i)*dimY + (j)] - P2_old[(dimX*dimY)*k + (i)*dimY + (j)]); + R3[(dimX*dimY)*k + (i)*dimY + (j)] = P3[(dimX*dimY)*k + (i)*dimY + (j)] + multip*(P3[(dimX*dimY)*k + (i)*dimY + (j)] - P3_old[(dimX*dimY)*k + (i)*dimY + (j)]); + }}} + return 1; +} + +/* General Functions */ +/*****************************************************************/ +/* Copy Image */ +float copyIm(float *A, float *B, int dimX, int dimY, int dimZ) +{ + int j; +#pragma omp parallel for shared(A, B) private(j) + for(j=0; j<dimX*dimY*dimZ; j++) B[j] = A[j]; + return *B; +} diff --git a/main_func/FISTA_REC.m b/main_func/FISTA_REC.m index 79369a5..ed74181 100644 --- a/main_func/FISTA_REC.m +++ b/main_func/FISTA_REC.m @@ -1,34 +1,36 @@ -function [X, error, objective, residual] = FISTA_REC(params) +function [X, output] = FISTA_REC(params) -% <<<< FISTA-based reconstruction algorithm using ASTRA-toolbox (parallel beam) >>>> +% <<<< FISTA-based reconstruction algorithm using ASTRA-toolbox >>>> % ___Input___: % params.[] file: -% - .sino (2D or 3D sinogram) [required] -% - .N (image dimension) [required] -% - .angles (in radians) [required] +% - .proj_geom (geometry of the projector) [required] +% - .vol_geom (geometry of the reconstructed object) [required] +% - .sino (vectorized in 2D or 3D sinogram) [required] % - .iterFISTA (iterations for the main loop) % - .L_const (Lipschitz constant, default Power method) ) % - .X_ideal (ideal image, if given) -% - .weights (statisitcal weights, size of sinogram) +% - .weights (statisitcal weights, size of the sinogram) % - .ROI (Region-of-interest, only if X_ideal is given) -% - .lambdaTV (TV regularization parameter, default 0 - reg. TV is switched off) -% - .tol (tolerance to terminate TV regularization, default 1.0e-04) -% - .iterTV (iterations for the TV penalty, default 0) -% - .lambdaHO (Higher Order LLT regularization parameter, default 0 - LLT reg. switched off) -% - .iterHO (iterations for HO penalty, default 50) -% - .tauHO (time step parameter for HO term) -% - .lambdaR_L1 (regularization parameter for L1 ring minimization, if lambdaR_L1 > 0 then switch on ring removal, default 0) -% - .alpha_ring (larger values can accelerate convergence but check stability, default 1) +% - .Regul_LambdaTV (TV regularization parameter, default 0 - reg. TV is switched off) +% - .Regul_tol (tolerance to terminate TV regularization, default 1.0e-04) +% - .Regul_iterTV (iterations for the TV penalty, default 0) +% - .Regul_LambdaHO (Higher Order LLT regularization parameter, default 0 - LLT reg. switched off) +% - .Regul_iterHO (iterations for HO penalty, default 50) +% - .Regul_tauHO (time step parameter for HO term) +% - .Ring_LambdaR_L1 (regularization parameter for L1 ring minimization, if lambdaR_L1 > 0 then switch on ring removal, default 0) +% - .Ring_Alpha (larger values can accelerate convergence but check stability, default 1) % - .fidelity (choose between "LS" and "student" data fidelities) +% - .initializ (a 'warm start' using SIRT method from ASTRA) % - .precondition (1 - switch on Fourier filtering before backprojection) % - .show (visualize reconstruction 1/0, (0 default)) % - .maxvalplot (maximum value to use for imshow[0 maxvalplot]) % - .slice (for 3D volumes - slice number to imshow) % ___Output___: % 1. X - reconstructed image/volume -% 2. error - residual error (if X_ideal is given) +% 2. Resid_error - residual error (if X_ideal is given) % 3. value of the objective function -% 4. forward projection(X) +% 4. forward projection of X + % References: % 1. "A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse % Problems" by A. Beck and M Teboulle @@ -38,49 +40,53 @@ function [X, error, objective, residual] = FISTA_REC(params) % D. Kazantsev, 2016-17 % Dealing with input parameters -if (isfield(params,'sino')) - sino = params.sino; - [anglesNumb, Detectors, SlicesZ] = size(sino); - fprintf('%s %i %s %i %s %i %s \n', 'Sinogram has a dimension of', anglesNumb, 'projections;', Detectors, 'detectors;', SlicesZ, 'vertical slices.'); +if (isfield(params,'proj_geom') == 0) + error('%s \n', 'Please provide ASTRA projection geometry - proj_geom'); else - fprintf('%s \n', 'Please provide a sinogram'); + proj_geom = params.proj_geom; end -if (isfield(params,'N')) - N = params.N; +if (isfield(params,'vol_geom') == 0) + error('%s \n', 'Please provide ASTRA object geometry - vol_geom'); else - fprintf('%s \n', 'Please provide N-size for the reconstructed image [N x N]'); + vol_geom = params.vol_geom; end -if (isfield(params,'N')) - angles = params.angles; - if (length(angles) ~= anglesNumb) - fprintf('%s \n', 'Sinogram angular dimension does not correspond to the angles dimension provided'); - end +N = params.vol_geom.GridColCount; +if (isfield(params,'sino')) + sino = params.sino; + [Detectors, anglesNumb, SlicesZ] = size(sino); + fprintf('%s %i %s %i %s %i %s \n', 'Sinogram has a dimension of', Detectors, 'detectors;', anglesNumb, 'projections;', SlicesZ, 'vertical slices.'); else - fprintf('%s \n', 'Please provide a vector of angles'); + error('%s \n', 'Please provide a sinogram'); end if (isfield(params,'iterFISTA')) iterFISTA = params.iterFISTA; else iterFISTA = 30; end +if (isfield(params,'weights')) + weights = params.weights; +else + weights = ones(size(sino)); +end if (isfield(params,'L_const')) L_const = params.L_const; else % using Power method (PM) to establish L constant - vol_geom = astra_create_vol_geom(N, N); - proj_geom = astra_create_proj_geom('parallel', 1.0, Detectors, angles); - - niter = 10; % number of iteration for PM - x = rand(N,N); - [sino_id, y] = astra_create_sino_cuda(x, proj_geom, vol_geom); - astra_mex_data2d('delete', sino_id); + niter = 5; % number of iteration for PM + x = rand(N,N,SlicesZ); + sqweight = sqrt(weights); + [sino_id, y] = astra_create_sino3d_cuda(x, proj_geom, vol_geom); + y = sqweight.*y; + astra_mex_data3d('delete', sino_id); for i = 1:niter - x = astra_create_backprojection_cuda(y, proj_geom, vol_geom); - s = norm(x); + [id,x] = astra_create_backprojection3d_cuda(sqweight.*y, proj_geom, vol_geom); + s = norm(x(:)); x = x/s; - [sino_id, y] = astra_create_sino_cuda(x, proj_geom, vol_geom); - astra_mex_data2d('delete', sino_id); + [sino_id, y] = astra_create_sino3d_cuda(x, proj_geom, vol_geom); + y = sqweight.*y; + astra_mex_data3d('delete', sino_id); + astra_mex_data3d('delete', id); end L_const = s; end @@ -89,53 +95,48 @@ if (isfield(params,'X_ideal')) else X_ideal = 'none'; end -if (isfield(params,'weights')) - weights = params.weights; -else - weights = 1; -end if (isfield(params,'ROI')) ROI = params.ROI; else ROI = find(X_ideal>=0.0); end -if (isfield(params,'lambdaTV')) - lambdaTV = params.lambdaTV; +if (isfield(params,'Regul_LambdaTV')) + lambdaTV = params.Regul_LambdaTV; else lambdaTV = 0; end -if (isfield(params,'tol')) - tol = params.tol; +if (isfield(params,'Regul_tol')) + tol = params.Regul_tol; else tol = 1.0e-04; end -if (isfield(params,'iterTV')) - iterTV = params.iterTV; +if (isfield(params,'Regul_iterTV')) + iterTV = params.Regul_iterTV; else - iterTV = 10; + iterTV = 25; end -if (isfield(params,'lambdaHO')) - lambdaHO = params.lambdaHO; +if (isfield(params,'Regul_LambdaHO')) + lambdaHO = params.Regul_LambdaHO; else lambdaHO = 0; end -if (isfield(params,'iterHO')) - iterHO = params.iterHO; +if (isfield(params,'Regul_iterHO')) + iterHO = params.Regul_iterHO; else iterHO = 50; end -if (isfield(params,'tauHO')) - tauHO = params.tauHO; +if (isfield(params,'Regul_tauHO')) + tauHO = params.Regul_tauHO; else tauHO = 0.0001; end -if (isfield(params,'lambdaR_L1')) - lambdaR_L1 = params.lambdaR_L1; +if (isfield(params,'Ring_LambdaR_L1')) + lambdaR_L1 = params.Ring_LambdaR_L1; else lambdaR_L1 = 0; end -if (isfield(params,'alpha_ring')) - alpha_ring = params.alpha_ring; % higher values can accelerate ring removal procedure +if (isfield(params,'Ring_Alpha')) + alpha_ring = params.Ring_Alpha; % higher values can accelerate ring removal procedure else alpha_ring = 1; end @@ -164,21 +165,43 @@ if (isfield(params,'slice')) else slice = 1; end +if (isfield(params,'initilize')) + % Create a data object for the reconstruction + rec_id = astra_mex_data3d('create', '-vol', vol_geom); + + sinogram_id = astra_mex_data3d('create', '-proj3d', proj_geom, sino); + + % Set up the parameters for a reconstruction algorithm using the GPU + cfg = astra_struct('SIRT3D_CUDA'); + cfg.ReconstructionDataId = rec_id; + cfg.ProjectionDataId = sinogram_id; + + % Create the algorithm object from the configuration structure + alg_id = astra_mex_algorithm('create', cfg); + astra_mex_algorithm('iterate', alg_id, 35); + % Get the result + X = astra_mex_data3d('get', rec_id); + + % Clean up. Note that GPU memory is tied up in the algorithm object, + % and main RAM in the data objects. + astra_mex_algorithm('delete', alg_id); + astra_mex_data3d('delete', rec_id); + astra_mex_data3d('delete', sinogram_id); +else + X = zeros(N,N,SlicesZ, 'single'); % storage for the solution +end + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% building geometry (parallel-beam) -vol_geom = astra_create_vol_geom(N, N); -proj_geom = astra_create_proj_geom('parallel', 1.0, Detectors, angles); -error = zeros(iterFISTA,1); % error vector +Resid_error = zeros(iterFISTA,1); % error vector objective = zeros(iterFISTA,1); % obhective vector if (lambdaR_L1 > 0) % do reconstruction WITH ring removal (Group-Huber fidelity) t = 1; - X = zeros(N,N,SlicesZ, 'single'); X_t = X; - add_ring = zeros(anglesNumb, Detectors, SlicesZ, 'single'); % size of sinogram array + add_ring = zeros(size(sino),'single'); % size of sinogram array r = zeros(Detectors,SlicesZ, 'single'); % 2D array (for 3D data) of sparse "ring" vectors r_x = r; @@ -189,47 +212,40 @@ if (lambdaR_L1 > 0) t_old = t; r_old = r; - % all slices loop - for j = 1:SlicesZ - - [sino_id, sino_updt] = astra_create_sino_cuda(X_t(:,:,j), proj_geom, vol_geom); - - for kkk = 1:anglesNumb - add_ring(kkk,:,j) = sino(kkk,:,j) - alpha_ring.*r_x(:,j)'; - end - - residual = sino_updt - add_ring(:,:,j); - - if (precondition == 1) - residual = filtersinc(residual'); % filtering residual (Fourier preconditioning) - residual = residual'; - end - - vec = sum(residual); - r(:,j) = r_x(:,j) - (1/L_const).*vec'; - - x_temp = astra_create_backprojection_cuda(residual, proj_geom, vol_geom); - - X(:,:,j) = X_t(:,:,j) - (1/L_const).*x_temp; - astra_mex_data2d('delete', sino_id); + [sino_id, sino_updt] = astra_create_sino3d_cuda(X_t, proj_geom, vol_geom); + + for kkk = 1:anglesNumb + add_ring(:,kkk,:) = sino(:,kkk,:) - alpha_ring.*r_x; + end + + residual = weights.*(sino_updt - add_ring); + + if (precondition == 1) + residual = filtersinc(residual'); % filtering residual (Fourier preconditioning) + residual = residual'; end + vec = sum(residual,2); + + r = r_x - (1./L_const).*vec; + + [id, x_temp] = astra_create_backprojection3d_cuda(residual, proj_geom, vol_geom); + + X = X_t - (1/L_const).*x_temp; + astra_mex_data3d('delete', sino_id); + astra_mex_data3d('delete', id); + if ((lambdaTV > 0) && (lambdaHO == 0)) - if (size(X,3) > 1) - [X] = FISTA_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA - gradTV = 1; - else - [X, gradTV] = FISTA_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA - end - objective(i) = 0.5.*norm(residual(:))^2 + norm(gradTV(:)); + [X, f_val] = FGP_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA + objective(i) = 0.5.*norm(residual(:))^2 + f_val; % X = SplitBregman_TV(single(X), lambdaTV, iterTV, tol); % TV-Split Bregman regularization on CPU (memory limited) elseif ((lambdaHO > 0) && (lambdaTV == 0)) % Higher Order regularization X = LLT_model(single(X), lambdaHO, tauHO, iterHO, tol, 0); % LLT higher order model elseif ((lambdaTV > 0) && (lambdaHO > 0)) %X1 = SplitBregman_TV(single(X), lambdaTV, iterTV, tol); % TV-Split Bregman regularization on CPU (memory limited) - X1 = FISTA_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA - X2 = LLT_model(single(X), lambdaHO, tauHO, iterHO, tol, 0); % LLT higher order model + X1 = FGP_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA + X2 = LLT_model(single(X), lambdaHO, tauHO, iterHO, 3.0e-05, 0); % LLT higher order model X = 0.5.*(X1 + X2); % averaged combination of two solutions elseif ((lambdaTV == 0) && (lambdaHO == 0)) objective(i) = 0.5.*norm(residual(:))^2; @@ -244,11 +260,11 @@ if (lambdaR_L1 > 0) if (show == 1) figure(10); imshow(X(:,:,slice), [0 maxvalplot]); figure(11); plot(r); title('Rings offset vector') - pause(0.03); + pause(0.03); end if (strcmp(X_ideal, 'none' ) == 0) - error(i) = RMSE(X(ROI), X_ideal(ROI)); - fprintf('%s %i %s %s %.4f %s %s %.4f \n', 'Iteration Number:', i, '|', 'Error RMSE:', error(i), '|', 'Objective:', objective(i)); + Resid_error(i) = RMSE(X(ROI), X_ideal(ROI)); + fprintf('%s %i %s %s %.4f %s %s %.4f \n', 'Iteration Number:', i, '|', 'Error RMSE:', Resid_error(i), '|', 'Objective:', objective(i)); else fprintf('%s %i %s %s %.4f \n', 'Iteration Number:', i, '|', 'Objective:', objective(i)); end @@ -258,50 +274,42 @@ if (lambdaR_L1 > 0) else % WITHOUT ring removal t = 1; - X = zeros(N,N,SlicesZ, 'single'); X_t = X; - % iterations loop + % FISTA outer iterations loop for i = 1:iterFISTA X_old = X; t_old = t; - % slices loop - for j = 1:SlicesZ - [sino_id, sino_updt] = astra_create_sino_cuda(X_t(:,:,j), proj_geom, vol_geom); - residual = weights.*(sino_updt - sino(:,:,j)); - - % employ students t fidelity term - if (strcmp(fidelity,'student') == 1) - res_vec = reshape(residual, anglesNumb*Detectors,1); - %s = 100; - %gr = (2)*res_vec./(s*2 + conj(res_vec).*res_vec); - [ff, gr] = studentst(res_vec,1); - residual = reshape(gr, anglesNumb, Detectors); - end - - if (precondition == 1) - residual = filtersinc(residual'); % filtering residual (Fourier preconditioning) - residual = residual'; - end - - x_temp = astra_create_backprojection_cuda(residual, proj_geom, vol_geom); - X(:,:,j) = X_t(:,:,j) - (1/L_const).*x_temp; - astra_mex_data2d('delete', sino_id); + [sino_id, sino_updt] = astra_create_sino3d_cuda(X_t, proj_geom, vol_geom); + residual = weights.*(sino_updt - sino); + + % employ students t fidelity term + if (strcmp(fidelity,'student') == 1) + res_vec = reshape(residual, anglesNumb*Detectors*SlicesZ,1); + %s = 100; + %gr = (2)*res_vec./(s*2 + conj(res_vec).*res_vec); + [ff, gr] = studentst(res_vec,1); + residual = reshape(gr, Detectors, anglesNumb, SlicesZ); + end + + if (precondition == 1) + residual = filtersinc(residual'); % filtering residual (Fourier preconditioning) + residual = residual'; end + [id, x_temp] = astra_create_backprojection3d_cuda(residual, proj_geom, vol_geom); + X = X_t - (1/L_const).*x_temp; + astra_mex_data3d('delete', sino_id); + astra_mex_data3d('delete', id); + if ((lambdaTV > 0) && (lambdaHO == 0)) - if (size(X,3) > 1) - [X] = FISTA_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA - gradTV = 1; - else - [X, gradTV] = FISTA_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA - end + [X,f_val] = FGP_TV(single(X), lambdaTV, iterTV, tol); % TV regularization using FISTA if (strcmp(fidelity,'student') == 1) - objective(i) = ff + norm(gradTV(:)); + objective(i) = ff + f_val; else - objective(i) = 0.5.*norm(residual(:))^2 + norm(gradTV(:)); + objective(i) = 0.5.*norm(residual(:))^2 + f_val; end % X = SplitBregman_TV(single(X), lambdaTV, iterTV, tol); % TV-Split Bregman regularization on CPU (memory limited) elseif ((lambdaHO > 0) && (lambdaTV == 0)) @@ -315,24 +323,25 @@ else objective(i) = 0.5.*norm(residual(:))^2; end - t = (1 + sqrt(1 + 4*t^2))/2; % updating t X_t = X + ((t_old-1)/t).*(X - X_old); % updating X if (show == 1) figure(11); imshow(X(:,:,slice), [0 maxvalplot]); - pause(0.03); + pause(0.03); end if (strcmp(X_ideal, 'none' ) == 0) - error(i) = RMSE(X(ROI), X_ideal(ROI)); - fprintf('%s %i %s %s %.4f %s %s %.4f \n', 'Iteration Number:', i, '|', 'Error RMSE:', error(i), '|', 'Objective:', objective(i)); + Resid_error(i) = RMSE(X(ROI), X_ideal(ROI)); + fprintf('%s %i %s %s %.4f %s %s %.4f \n', 'Iteration Number:', i, '|', 'Error RMSE:', Resid_error(i), '|', 'Objective:', objective(i)); else fprintf('%s %i %s %s %.4f \n', 'Iteration Number:', i, '|', 'Objective:', objective(i)); end - end end +output.Resid_error = Resid_error; +output.objective = objective; +output.L_const = L_const; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end diff --git a/main_func/FISTA_TV.c b/main_func/FISTA_TV.c deleted file mode 100644 index 87681bc..0000000 --- a/main_func/FISTA_TV.c +++ /dev/null @@ -1,331 +0,0 @@ -#include "mex.h" -#include <matrix.h> -#include <math.h> -#include <stdlib.h> -#include <memory.h> -#include <stdio.h> -#include "omp.h" - -/* C-OMP implementation of FISTA-TV denoising-regularization model (2D/3D) - * - * Input Parameters: - * 1. Noisy image/volume - * 2. lambda - regularization parameter - * 3. Number of iterations - * 4. eplsilon - tolerance constant - * - * Output: - * Filtered/regularized image - * - * Example: - * figure; - * Im = double(imread('lena_gray_256.tif'))/255; % loading image - * u0 = Im + .05*randn(size(Im)); % adding noise - * u = FISTA_TV(single(u0), 0.05, 150, 1e-04); - * - * to compile with OMP support: mex FISTA_TV.c CFLAGS="\$CFLAGS -fopenmp -Wall" LDFLAGS="\$LDFLAGS -fopenmp" - * References: A. Beck & M. Teboulle - * - * D. Kazantsev, 2016* - */ - -float copyIm(float *A, float *B, int dimX, int dimY, int dimZ); -float Obj_func2D(float *A, float *D, float *R1, float *R2, float *grad, float lambda, int dimX, int dimY); -float Grad_func2D(float *P1, float *P2, float *D, float *R1, float *R2, float lambda, int dimX, int dimY); -float Proj_func2D(float *P1, float *P2, int dimX, int dimY); -float Rupd_func2D(float *P1, float *P1_old, float *P2, float *P2_old, float *R1, float *R2, float tkp1, float tk, int dimX, int dimY); - -float Obj_func3D(float *A, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ); -float Grad_func3D(float *P1, float *P2, float *P3, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ); -float Proj_func3D(float *P1, float *P2, float *P3, int dimX, int dimY, int dimZ); -float Rupd_func3D(float *P1, float *P1_old, float *P2, float *P2_old, float *P3, float *P3_old, float *R1, float *R2, float *R3, float tkp1, float tk, int dimX, int dimY, int dimZ); - - -void mexFunction( - int nlhs, mxArray *plhs[], - int nrhs, const mxArray *prhs[]) - -{ - int number_of_dims, iter, dimX, dimY, dimZ, ll, j, count; - const int *dim_array; - float *A, *grad=NULL, *D=NULL, *D_old=NULL, *P1=NULL, *P2=NULL, *P3=NULL, *P1_old=NULL, *P2_old=NULL, *P3_old=NULL, *R1=NULL, *R2=NULL, *R3=NULL, lambda, tk, tkp1, re, re1, re_old, epsil; - - number_of_dims = mxGetNumberOfDimensions(prhs[0]); - dim_array = mxGetDimensions(prhs[0]); - - if(nrhs != 4) mexErrMsgTxt("Four input parameters is reqired: Image(2D/3D), Regularization parameter, Iterations, Tolerance"); - - /*Handling Matlab input data*/ - A = (float *) mxGetData(prhs[0]); /*noisy image (2D/3D) */ - lambda = (float) mxGetScalar(prhs[1]); /* regularization parameter */ - iter = (int) mxGetScalar(prhs[2]); /* iterations number */ - epsil = (float) mxGetScalar(prhs[3]); /* tolerance constant */ - - /*Handling Matlab output data*/ - dimX = dim_array[0]; dimY = dim_array[1]; dimZ = dim_array[2]; - - tk = 1.0f; - tkp1=1.0f; - count = 1; - re_old = 0.0f; - - if (number_of_dims == 2) { - dimZ = 1; /*2D case*/ - D = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); - grad = (float*)mxGetPr(plhs[1] = mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); - D_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); - P1 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); - P2 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); - P1_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); - P2_old = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); - R1 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); - R2 = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); - - /* begin iterations */ - for(ll=0; ll<iter; ll++) { - - /*storing old values*/ - copyIm(D, D_old, dimX, dimY, dimZ); - copyIm(P1, P1_old, dimX, dimY, dimZ); - copyIm(P2, P2_old, dimX, dimY, dimZ); - tk = tkp1; - - /* computing the gradient of the objective function */ - Obj_func2D(A, D, R1, R2, grad, lambda, dimX, dimY); - - /*Taking a step towards minus of the gradient*/ - Grad_func2D(P1, P2, D, R1, R2, lambda, dimX, dimY); - - /* projection step */ - Proj_func2D(P1, P2, dimX, dimY); - - /*updating R and t*/ - tkp1 = (1.0f + sqrt(1.0f + 4.0f*tk*tk))*0.5f; - Rupd_func2D(P1, P1_old, P2, P2_old, R1, R2, tkp1, tk, dimX, dimY); - - /* calculate norm */ - re = 0.0f; re1 = 0.0f; - for(j=0; j<dimX*dimY*dimZ; j++) - { - re += pow(D[j] - D_old[j],2); - re1 += pow(D[j],2); - } - re = sqrt(re)/sqrt(re1); - if (re < epsil) count++; - if (count > 3) break; - - /* check that the residual norm is decreasing */ - if (ll > 2) { - if (re > re_old) break; } - - re_old = re; - /*printf("%f %i %i \n", re, ll, count); */ - } - printf("TV iterations stopped at iteration: %i\n", ll); - } - if (number_of_dims == 3) { - D = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); - D_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); - P1 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); - P2 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); - P3 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); - P1_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); - P2_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); - P3_old = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); - R1 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); - R2 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); - R3 = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); - - /* begin iterations */ - for(ll=0; ll<iter; ll++) { - - /*storing old values*/ - copyIm(D, D_old, dimX, dimY, dimZ); - copyIm(P1, P1_old, dimX, dimY, dimZ); - copyIm(P2, P2_old, dimX, dimY, dimZ); - copyIm(P3, P3_old, dimX, dimY, dimZ); - - tk = tkp1; - - /* computing the gradient of the objective function */ - Obj_func3D(A, D, R1, R2, R3,lambda, dimX, dimY, dimZ); - - /*Taking a step towards minus of the gradient*/ - Grad_func3D(P1, P2, P3, D, R1, R2, R3, lambda, dimX, dimY, dimZ); - - /* projection step */ - Proj_func3D(P1, P2, P3, dimX, dimY, dimZ); - - /*updating R and t*/ - tkp1 = (1.0f + sqrt(1.0f + 4.0f*tk*tk))*0.5f; - Rupd_func3D(P1, P1_old, P2, P2_old, P3, P3_old, R1, R2, R3, tkp1, tk, dimX, dimY, dimZ); - - /* calculate norm - stopping rules*/ - re = 0.0f; re1 = 0.0f; - for(j=0; j<dimX*dimY*dimZ; j++) - { - re += pow(D[j] - D_old[j],2); - re1 += pow(D[j],2); - } - re = sqrt(re)/sqrt(re1); - /* stop if the norm residual is less than the tolerance EPS */ - if (re < epsil) count++; - if (count > 3) break; - - /* check that the residual norm is decreasing */ - if (ll > 2) { - if (re > re_old) break; } - - re_old = re; - /*printf("%f %i %i \n", re, ll, count); */ - } - printf("TV iterations stopped at iteration: %i\n", ll); - } -} - -/* 2D-case related Functions */ -/*****************************************************************/ -float Obj_func2D(float *A, float *D, float *R1, float *R2, float *grad, float lambda, int dimX, int dimY) -{ - float val1, val2; - int i,j; -#pragma omp parallel for shared(A,D,R1,R2) private(i,j,val1,val2) - for(i=0; i<dimX; i++) { - for(j=0; j<dimY; j++) { - /* symmetric boundary conditions (Neuman) */ - if (i == 0) {val1 = R1[(i+1)*dimY + (j)];} else {val1 = R1[(i-1)*dimY + (j)];} - if (j == 0) {val2 = R2[(i)*dimY + (j+1)];} else {val2 = R2[(i)*dimY + (j-1)];} - D[(i)*dimY + (j)] = A[(i)*dimY + (j)] - lambda*(R1[(i)*dimY + (j)] + R2[(i)*dimY + (j)] - val1 - val2); - grad[(i)*dimY + (j)] = lambda*(R1[(i)*dimY + (j)] + R2[(i)*dimY + (j)] - val1 - val2); - }} - return *D; -} -float Grad_func2D(float *P1, float *P2, float *D, float *R1, float *R2, float lambda, int dimX, int dimY) -{ - float val1, val2; - int i,j; -#pragma omp parallel for shared(P1,P2,D,R1,R2) private(i,j,val1,val2) - for(i=0; i<dimX; i++) { - for(j=0; j<dimY; j++) { - /* symmetric boundary conditions (Neuman) */ - - if (i == dimX-1) {val1 = D[(i)*dimY + (j)] - D[(i-1)*dimY + (j)];} else {val1 = D[(i)*dimY + (j)] - D[(i+1)*dimY + (j)];} - if (j == dimY-1) {val2 = D[(i)*dimY + (j)] - D[(i)*dimY + (j-1)];} else {val2 = D[(i)*dimY + (j)] - D[(i)*dimY + (j+1)];} - - P1[(i)*dimY + (j)] = R1[(i)*dimY + (j)] + (1.0f/(8.0f*lambda))*val1; - P2[(i)*dimY + (j)] = R2[(i)*dimY + (j)] + (1.0f/(8.0f*lambda))*val2; - }} - return 1; -} -float Proj_func2D(float *P1, float *P2, int dimX, int dimY) -{ - float val1, val2; - int i,j; -#pragma omp parallel for shared(P1,P2) private(i,j,val1,val2) - for(i=0; i<dimX; i++) { - for(j=0; j<dimY; j++) { - val1 = fabs(P1[(i)*dimY + (j)]); - val2 = fabs(P2[(i)*dimY + (j)]); - if (val1 < 1.0f) {val1 = 1.0f;} - if (val2 < 1.0f) {val2 = 1.0f;} - - P1[(i)*dimY + (j)] = P1[(i)*dimY + (j)]/val1; - P2[(i)*dimY + (j)] = P2[(i)*dimY + (j)]/val2; - }} - return 1; -} -float Rupd_func2D(float *P1, float *P1_old, float *P2, float *P2_old, float *R1, float *R2, float tkp1, float tk, int dimX, int dimY) -{ - int i,j; -#pragma omp parallel for shared(P1,P2,P1_old,P2_old,R1,R2) private(i,j) - for(i=0; i<dimX; i++) { - for(j=0; j<dimY; j++) { - R1[(i)*dimY + (j)] = P1[(i)*dimY + (j)] + ((tk-1.0f)/tkp1)*(P1[(i)*dimY + (j)] - P1_old[(i)*dimY + (j)]); - R2[(i)*dimY + (j)] = P2[(i)*dimY + (j)] + ((tk-1.0f)/tkp1)*(P2[(i)*dimY + (j)] - P2_old[(i)*dimY + (j)]); - }} - return 1; -} - - -/* 3D-case related Functions */ -/*****************************************************************/ -float Obj_func3D(float *A, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ) -{ - float val1, val2, val3; - int i,j,k; -#pragma omp parallel for shared(A,D,R1,R2,R3) private(i,j,k,val1,val2,val3) - for(i=0; i<dimX; i++) { - for(j=0; j<dimY; j++) { - for(k=0; k<dimZ; k++) { - /* symmetric boundary conditions (Neuman) */ - if (i == 0) {val1 = R1[(dimX*dimY)*k + (i+1)*dimY + (j)];} else {val1 = R1[(dimX*dimY)*k + (i-1)*dimY + (j)];} - if (j == 0) {val2 = R2[(dimX*dimY)*k + (i)*dimY + (j+1)];} else {val2 = R2[(dimX*dimY)*k + (i)*dimY + (j-1)];} - if (k == 0) {val3 = R3[(dimX*dimY)*(k+1) + (i)*dimY + (j)];} else {val3 = R3[(dimX*dimY)*(k-1) + (i)*dimY + (j)];} - D[(dimX*dimY)*k + (i)*dimY + (j)] = A[(dimX*dimY)*k + (i)*dimY + (j)] - lambda*(R1[(dimX*dimY)*k + (i)*dimY + (j)] + R2[(dimX*dimY)*k + (i)*dimY + (j)] + R3[(dimX*dimY)*k + (i)*dimY + (j)] - val1 - val2 - val3); - }}} - return *D; -} -float Grad_func3D(float *P1, float *P2, float *P3, float *D, float *R1, float *R2, float *R3, float lambda, int dimX, int dimY, int dimZ) -{ - float val1, val2, val3; - int i,j,k; -#pragma omp parallel for shared(P1,P2,P3,D,R1,R2,R3) private(i,j,k,val1,val2,val3) - for(i=0; i<dimX; i++) { - for(j=0; j<dimY; j++) { - for(k=0; k<dimZ; k++) { - /* symmetric boundary conditions (Neuman) */ - if (i == dimX-1) {val1 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*k + (i-1)*dimY + (j)];} else {val1 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*k + (i+1)*dimY + (j)];} - if (j == dimY-1) {val2 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*k + (i)*dimY + (j-1)];} else {val2 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*k + (i)*dimY + (j+1)];} - if (k == dimZ-1) {val3 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*(k-1) + (i)*dimY + (j)];} else {val3 = D[(dimX*dimY)*k + (i)*dimY + (j)] - D[(dimX*dimY)*(k+1) + (i)*dimY + (j)];} - - P1[(dimX*dimY)*k + (i)*dimY + (j)] = R1[(dimX*dimY)*k + (i)*dimY + (j)] + (1.0f/(8.0f*lambda))*val1; - P2[(dimX*dimY)*k + (i)*dimY + (j)] = R2[(dimX*dimY)*k + (i)*dimY + (j)] + (1.0f/(8.0f*lambda))*val2; - P3[(dimX*dimY)*k + (i)*dimY + (j)] = R3[(dimX*dimY)*k + (i)*dimY + (j)] + (1.0f/(8.0f*lambda))*val3; - }}} - return 1; -} -float Proj_func3D(float *P1, float *P2, float *P3, int dimX, int dimY, int dimZ) -{ - float val1, val2, val3; - int i,j,k; -#pragma omp parallel for shared(P1,P2,P3) private(i,j,k,val1,val2,val3) - for(i=0; i<dimX; i++) { - for(j=0; j<dimY; j++) { - for(k=0; k<dimZ; k++) { - val1 = fabs(P1[(dimX*dimY)*k + (i)*dimY + (j)]); - val2 = fabs(P2[(dimX*dimY)*k + (i)*dimY + (j)]); - val3 = fabs(P3[(dimX*dimY)*k + (i)*dimY + (j)]); - if (val1 < 1.0f) {val1 = 1.0f;} - if (val2 < 1.0f) {val2 = 1.0f;} - if (val3 < 1.0f) {val3 = 1.0f;} - - P1[(dimX*dimY)*k + (i)*dimY + (j)] = P1[(dimX*dimY)*k + (i)*dimY + (j)]/val1; - P2[(dimX*dimY)*k + (i)*dimY + (j)] = P2[(dimX*dimY)*k + (i)*dimY + (j)]/val2; - P3[(dimX*dimY)*k + (i)*dimY + (j)] = P3[(dimX*dimY)*k + (i)*dimY + (j)]/val3; - }}} - return 1; -} -float Rupd_func3D(float *P1, float *P1_old, float *P2, float *P2_old, float *P3, float *P3_old, float *R1, float *R2, float *R3, float tkp1, float tk, int dimX, int dimY, int dimZ) -{ - int i,j,k; -#pragma omp parallel for shared(P1,P2,P3,P1_old,P2_old,P3_old,R1,R2,R3) private(i,j,k) - for(i=0; i<dimX; i++) { - for(j=0; j<dimY; j++) { - for(k=0; k<dimZ; k++) { - R1[(dimX*dimY)*k + (i)*dimY + (j)] = P1[(dimX*dimY)*k + (i)*dimY + (j)] + ((tk-1.0f)/tkp1)*(P1[(dimX*dimY)*k + (i)*dimY + (j)] - P1_old[(dimX*dimY)*k + (i)*dimY + (j)]); - R2[(dimX*dimY)*k + (i)*dimY + (j)] = P2[(dimX*dimY)*k + (i)*dimY + (j)] + ((tk-1.0f)/tkp1)*(P2[(dimX*dimY)*k + (i)*dimY + (j)] - P2_old[(dimX*dimY)*k + (i)*dimY + (j)]); - R3[(dimX*dimY)*k + (i)*dimY + (j)] = P3[(dimX*dimY)*k + (i)*dimY + (j)] + ((tk-1.0f)/tkp1)*(P3[(dimX*dimY)*k + (i)*dimY + (j)] - P3_old[(dimX*dimY)*k + (i)*dimY + (j)]); - }}} - return 1; -} - -/* General Functions */ -/*****************************************************************/ -/* Copy Image */ -float copyIm(float *A, float *B, int dimX, int dimY, int dimZ) -{ - int j; -#pragma omp parallel for shared(A, B) private(j) - for(j=0; j<dimX*dimY*dimZ; j++) B[j] = A[j]; - return *B; -}
\ No newline at end of file diff --git a/main_func/LLT_model.c b/main_func/LLT_model.c index a611e54..0aed31e 100644 --- a/main_func/LLT_model.c +++ b/main_func/LLT_model.c @@ -6,7 +6,7 @@ #include <stdio.h> #include "omp.h" -#define EPS 0.001 +#define EPS 0.01 /* C-OMP implementation of Lysaker, Lundervold and Tai (LLT) model of higher order regularization penalty * diff --git a/main_func/SplitBregman_TV.c b/main_func/SplitBregman_TV.c index 691ccce..f143aa6 100644 --- a/main_func/SplitBregman_TV.c +++ b/main_func/SplitBregman_TV.c @@ -11,8 +11,9 @@ * Input Parameters: * 1. Noisy image/volume * 2. lambda - regularization parameter - * 3. Number of iterations - * 4. eplsilon - tolerance constant + * 3. Number of iterations [OPTIONAL parameter] + * 4. eplsilon - tolerance constant [OPTIONAL parameter] + * 5. TV-type: 'iso' or 'l1' [OPTIONAL parameter] * * Output: * Filtered/regularized image @@ -31,12 +32,13 @@ float copyIm(float *A, float *B, int dimX, int dimY, int dimZ); float gauss_seidel2D(float *U, float *A, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda, float mu); -float updDxDy_shrink2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda); float updDxDy_shrinkAniso2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda); +float updDxDy_shrinkIso2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda); float updBxBy2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY); float gauss_seidel3D(float *U, float *A, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ, float lambda, float mu); -float updDxDyDz_shrink3D(float *U, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ, float lambda); +float updDxDyDz_shrinkAniso3D(float *U, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ, float lambda); +float updDxDyDz_shrinkIso3D(float *U, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ, float lambda); float updBxByBz3D(float *U, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ); void mexFunction( @@ -44,28 +46,39 @@ void mexFunction( int nrhs, const mxArray *prhs[]) { - int number_of_dims, iter, dimX, dimY, dimZ, ll, j, count; + int number_of_dims, iter, dimX, dimY, dimZ, ll, j, count, methTV; const int *dim_array; float *A, *U=NULL, *U_old=NULL, *Dx=NULL, *Dy=NULL, *Dz=NULL, *Bx=NULL, *By=NULL, *Bz=NULL, lambda, mu, epsil, re, re1, re_old; number_of_dims = mxGetNumberOfDimensions(prhs[0]); dim_array = mxGetDimensions(prhs[0]); - if(nrhs != 4) mexErrMsgTxt("Four input parameters is reqired: Image(2D/3D), Regularization parameter, Iterations, Tolerance"); + /*Handling Matlab input data*/ + if ((nrhs < 2) || (nrhs > 5)) mexErrMsgTxt("At least 2 parameters is required: Image(2D/3D), Regularization parameter. The full list of parameters: Image(2D/3D), Regularization parameter, iterations number, tolerance, penalty type ('iso' or 'l1')"); /*Handling Matlab input data*/ A = (float *) mxGetData(prhs[0]); /*noisy image (2D/3D) */ mu = (float) mxGetScalar(prhs[1]); /* regularization parameter */ - iter = (int) mxGetScalar(prhs[2]); /* iterations number */ - epsil = (float) mxGetScalar(prhs[3]); /* tolerance constant */ + iter = 35; /* default iterations number */ + epsil = 0.0001; /* default tolerance constant */ + methTV = 0; /* default isotropic TV penalty */ + if ((nrhs == 3) || (nrhs == 4) || (nrhs == 5)) iter = (int) mxGetScalar(prhs[2]); /* iterations number */ + if ((nrhs == 4) || (nrhs == 5)) epsil = (float) mxGetScalar(prhs[3]); /* tolerance constant */ + if (nrhs == 5) { + char *penalty_type; + penalty_type = mxArrayToString(prhs[4]); /* choosing TV penalty: 'iso' or 'l1', 'iso' is the default */ + if ((strcmp(penalty_type, "l1") != 0) && (strcmp(penalty_type, "iso") != 0)) mexErrMsgTxt("Choose TV type: 'iso' or 'l1',"); + if (strcmp(penalty_type, "l1") == 0) methTV = 1; /* enable 'l1' penalty */ + mxFree(penalty_type); + } + if (mxGetClassID(prhs[0]) != mxSINGLE_CLASS) {mexErrMsgTxt("The input image must be in a single precision"); } - lambda = 2.0f*2.0f; + lambda = 2.0f*mu; count = 1; - re_old = 0.0f; + re_old = 0.0f; /*Handling Matlab output data*/ dimY = dim_array[0]; dimX = dim_array[1]; dimZ = dim_array[2]; - if (number_of_dims == 2) { dimZ = 1; /*2D case*/ U = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); @@ -73,7 +86,7 @@ void mexFunction( Dx = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); Dy = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); Bx = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); - By = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); + By = (float*)mxGetPr(mxCreateNumericArray(2, dim_array, mxSINGLE_CLASS, mxREAL)); copyIm(A, U, dimX, dimY, dimZ); /*initialize */ @@ -82,13 +95,14 @@ void mexFunction( /*storing old values*/ copyIm(U, U_old, dimX, dimY, dimZ); - - gauss_seidel2D(U, A, Dx, Dy, Bx, By, dimX, dimY, lambda, mu); - - updDxDy_shrink2D(U, Dx, Dy, Bx, By, dimX, dimY, lambda); - //updDxDy_shrinkAniso2D(U, Dx, Dy, Bx, By, dimX, dimY, lambda); - updBxBy2D(U, Dx, Dy, Bx, By, dimX, dimY); + /*GS iteration */ + gauss_seidel2D(U, A, Dx, Dy, Bx, By, dimX, dimY, lambda, mu); + + if (methTV == 1) updDxDy_shrinkAniso2D(U, Dx, Dy, Bx, By, dimX, dimY, lambda); + else updDxDy_shrinkIso2D(U, Dx, Dy, Bx, By, dimX, dimY, lambda); + + updBxBy2D(U, Dx, Dy, Bx, By, dimX, dimY); /* calculate norm to terminate earlier */ re = 0.0f; re1 = 0.0f; @@ -97,20 +111,20 @@ void mexFunction( re += pow(U_old[j] - U[j],2); re1 += pow(U_old[j],2); } - re = sqrt(re)/sqrt(re1); + re = sqrt(re)/sqrt(re1); if (re < epsil) count++; - if (count > 4) break; + if (count > 4) break; /* check that the residual norm is decreasing */ if (ll > 2) { - if (re > re_old) break; + if (re > re_old) break; } - re_old = re; - /*printf("%f %i %i \n", re, ll, count); */ + re_old = re; + /*printf("%f %i %i \n", re, ll, count); */ - /*copyIm(U_old, U, dimX, dimY, dimZ); */ + /*copyIm(U_old, U, dimX, dimY, dimZ); */ } - printf("SB iterations stopped at iteration: %i\n", ll); + printf("SB iterations stopped at iteration: %i\n", ll); } if (number_of_dims == 3) { U = (float*)mxGetPr(plhs[0] = mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); @@ -119,22 +133,24 @@ void mexFunction( Dy = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); Dz = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); Bx = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); - By = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); - Bz = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); + By = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); + Bz = (float*)mxGetPr(mxCreateNumericArray(3, dim_array, mxSINGLE_CLASS, mxREAL)); copyIm(A, U, dimX, dimY, dimZ); /*initialize */ /* begin outer SB iterations */ for(ll=0; ll<iter; ll++) { - /*storing old values*/ - copyIm(U, U_old, dimX, dimY, dimZ); - - gauss_seidel3D(U, A, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ, lambda, mu); - - updDxDyDz_shrink3D(U, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ, lambda); + /*storing old values*/ + copyIm(U, U_old, dimX, dimY, dimZ); + + /*GS iteration */ + gauss_seidel3D(U, A, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ, lambda, mu); + + if (methTV == 1) updDxDyDz_shrinkAniso3D(U, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ, lambda); + else updDxDyDz_shrinkIso3D(U, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ, lambda); - updBxByBz3D(U, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ); + updBxByBz3D(U, Dx, Dy, Dz, Bx, By, Bz, dimX, dimY, dimZ); /* calculate norm to terminate earlier */ re = 0.0f; re1 = 0.0f; @@ -143,17 +159,17 @@ void mexFunction( re += pow(U[j] - U_old[j],2); re1 += pow(U[j],2); } - re = sqrt(re)/sqrt(re1); + re = sqrt(re)/sqrt(re1); if (re < epsil) count++; - if (count > 4) break; + if (count > 4) break; /* check that the residual norm is decreasing */ if (ll > 2) { if (re > re_old) break; } /*printf("%f %i %i \n", re, ll, count); */ - re_old = re; + re_old = re; } - printf("SB iterations stopped at iteration: %i\n", ll); + printf("SB iterations stopped at iteration: %i\n", ll); } } @@ -167,92 +183,92 @@ float gauss_seidel2D(float *U, float *A, float *Dx, float *Dy, float *Bx, float #pragma omp parallel for shared(U) private(i,j,i1,i2,j1,j2,sum) for(i=0; i<dimX; i++) { - /* symmetric boundary conditions (Neuman) */ - i1 = i+1; if (i1 == dimX) i1 = i-1; - i2 = i-1; if (i2 < 0) i2 = i+1; + /* symmetric boundary conditions (Neuman) */ + i1 = i+1; if (i1 == dimX) i1 = i-1; + i2 = i-1; if (i2 < 0) i2 = i+1; for(j=0; j<dimY; j++) { - /* symmetric boundary conditions (Neuman) */ + /* symmetric boundary conditions (Neuman) */ j1 = j+1; if (j1 == dimY) j1 = j-1; - j2 = j-1; if (j2 < 0) j2 = j+1; + j2 = j-1; if (j2 < 0) j2 = j+1; - sum = Dx[(i2)*dimY + (j)] - Dx[(i)*dimY + (j)] + Dy[(i)*dimY + (j2)] - Dy[(i)*dimY + (j)] - Bx[(i2)*dimY + (j)] + Bx[(i)*dimY + (j)] - By[(i)*dimY + (j2)] + By[(i)*dimY + (j)]; + sum = Dx[(i2)*dimY + (j)] - Dx[(i)*dimY + (j)] + Dy[(i)*dimY + (j2)] - Dy[(i)*dimY + (j)] - Bx[(i2)*dimY + (j)] + Bx[(i)*dimY + (j)] - By[(i)*dimY + (j2)] + By[(i)*dimY + (j)]; sum += (U[(i1)*dimY + (j)] + U[(i2)*dimY + (j)] + U[(i)*dimY + (j1)] + U[(i)*dimY + (j2)]); sum *= lambda; - sum += mu*A[(i)*dimY + (j)]; + sum += mu*A[(i)*dimY + (j)]; U[(i)*dimY + (j)] = normConst*sum; }} return *U; } -float updDxDy_shrink2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda) +float updDxDy_shrinkAniso2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda) { - int i,j,i1,j1; - float val1, val11, val2, val22; - - #pragma omp parallel for shared(U) private(i,j,i1,j1,val1,val11,val2,val22) - for(i=0; i<dimX; i++) { + int i,j,i1,j1; + float val1, val11, val2, val22, denom_lam; + denom_lam = 1.0f/lambda; +#pragma omp parallel for shared(U,denom_lam) private(i,j,i1,j1,val1,val11,val2,val22) + for(i=0; i<dimX; i++) { for(j=0; j<dimY; j++) { /* symmetric boundary conditions (Neuman) */ i1 = i+1; if (i1 == dimX) i1 = i-1; j1 = j+1; if (j1 == dimY) j1 = j-1; - + val1 = (U[(i1)*dimY + (j)] - U[(i)*dimY + (j)]) + Bx[(i)*dimY + (j)]; val2 = (U[(i)*dimY + (j1)] - U[(i)*dimY + (j)]) + By[(i)*dimY + (j)]; - val11 = fabs(val1) - 1.0f/lambda; if (val11 < 0) val11 = 0; - val22 = fabs(val2) - 1.0f/lambda; if (val22 < 0) val22 = 0; + val11 = fabs(val1) - denom_lam; if (val11 < 0) val11 = 0; + val22 = fabs(val2) - denom_lam; if (val22 < 0) val22 = 0; if (val1 !=0) Dx[(i)*dimY + (j)] = (val1/fabs(val1))*val11; else Dx[(i)*dimY + (j)] = 0; if (val2 !=0) Dy[(i)*dimY + (j)] = (val2/fabs(val2))*val22; else Dy[(i)*dimY + (j)] = 0; - }} + }} return 1; } -float updDxDy_shrinkAniso2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda) +float updDxDy_shrinkIso2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY, float lambda) { - int i,j,i1,j1; - float val1, val11, val2, denom, denom_lam; - denom_lam = 1.0f/lambda; - - #pragma omp parallel for shared(U) private(i,j,i1,j1,val1,val11,val2,denom,denom_lam) - for(i=0; i<dimX; i++) { + int i,j,i1,j1; + float val1, val11, val2, denom, denom_lam; + denom_lam = 1.0f/lambda; + +#pragma omp parallel for shared(U,denom_lam) private(i,j,i1,j1,val1,val11,val2,denom) + for(i=0; i<dimX; i++) { for(j=0; j<dimY; j++) { /* symmetric boundary conditions (Neuman) */ i1 = i+1; if (i1 == dimX) i1 = i-1; j1 = j+1; if (j1 == dimY) j1 = j-1; - + val1 = (U[(i1)*dimY + (j)] - U[(i)*dimY + (j)]) + Bx[(i)*dimY + (j)]; val2 = (U[(i)*dimY + (j1)] - U[(i)*dimY + (j)]) + By[(i)*dimY + (j)]; denom = sqrt(val1*val1 + val2*val2); - val11 = (denom - denom_lam); if (val11 < 0) val11 = 0.0f; - + val11 = (denom - denom_lam); if (val11 < 0) val11 = 0.0f; + if (denom != 0.0f) { - Dx[(i)*dimY + (j)] = val11*(val1/denom); - Dy[(i)*dimY + (j)] = val11*(val2/denom); - } + Dx[(i)*dimY + (j)] = val11*(val1/denom); + Dy[(i)*dimY + (j)] = val11*(val2/denom); + } else { Dx[(i)*dimY + (j)] = 0; Dy[(i)*dimY + (j)] = 0; } - }} + }} return 1; } float updBxBy2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, int dimY) { - int i,j,i1,j1; - #pragma omp parallel for shared(U) private(i,j,i1,j1) - for(i=0; i<dimX; i++) { + int i,j,i1,j1; +#pragma omp parallel for shared(U) private(i,j,i1,j1) + for(i=0; i<dimX; i++) { for(j=0; j<dimY; j++) { /* symmetric boundary conditions (Neuman) */ i1 = i+1; if (i1 == dimX) i1 = i-1; - j1 = j+1; if (j1 == dimY) j1 = j-1; + j1 = j+1; if (j1 == dimY) j1 = j-1; Bx[(i)*dimY + (j)] = Bx[(i)*dimY + (j)] + ((U[(i1)*dimY + (j)] - U[(i)*dimY + (j)]) - Dx[(i)*dimY + (j)]); - By[(i)*dimY + (j)] = By[(i)*dimY + (j)] + ((U[(i)*dimY + (j1)] - U[(i)*dimY + (j)]) - Dy[(i)*dimY + (j)]); - }} - return 1; + By[(i)*dimY + (j)] = By[(i)*dimY + (j)] + ((U[(i)*dimY + (j1)] - U[(i)*dimY + (j)]) - Dy[(i)*dimY + (j)]); + }} + return 1; } @@ -261,78 +277,115 @@ float updBxBy2D(float *U, float *Dx, float *Dy, float *Bx, float *By, int dimX, float gauss_seidel3D(float *U, float *A, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ, float lambda, float mu) { float normConst, d_val, b_val, sum; - int i,j,i1,i2,j1,j2,k,k1,k2; + int i,j,i1,i2,j1,j2,k,k1,k2; normConst = 1.0f/(mu + 6.0f*lambda); #pragma omp parallel for shared(U) private(i,j,i1,i2,j1,j2,k,k1,k2,d_val,b_val,sum) for(i=0; i<dimX; i++) { for(j=0; j<dimY; j++) { for(k=0; k<dimZ; k++) { - /* symmetric boundary conditions (Neuman) */ - i1 = i+1; if (i1 == dimX) i1 = i-1; - i2 = i-1; if (i2 < 0) i2 = i+1; - j1 = j+1; if (j1 == dimY) j1 = j-1; - j2 = j-1; if (j2 < 0) j2 = j+1; - k1 = k+1; if (k1 == dimZ) k1 = k-1; - k2 = k-1; if (k2 < 0) k2 = k+1; - - d_val = Dx[(dimX*dimY)*k + (i2)*dimY + (j)] - Dx[(dimX*dimY)*k + (i)*dimY + (j)] + Dy[(dimX*dimY)*k + (i)*dimY + (j2)] - Dy[(dimX*dimY)*k + (i)*dimY + (j)] + Dz[(dimX*dimY)*k2 + (i)*dimY + (j)] - Dz[(dimX*dimY)*k + (i)*dimY + (j)]; - b_val = -Bx[(dimX*dimY)*k + (i2)*dimY + (j)] + Bx[(dimX*dimY)*k + (i)*dimY + (j)] - By[(dimX*dimY)*k + (i)*dimY + (j2)] + By[(dimX*dimY)*k + (i)*dimY + (j)] - Bz[(dimX*dimY)*k2 + (i)*dimY + (j)] + Bz[(dimX*dimY)*k + (i)*dimY + (j)]; - sum = d_val + b_val; - sum += U[(dimX*dimY)*k + (i1)*dimY + (j)] + U[(dimX*dimY)*k + (i2)*dimY + (j)] + U[(dimX*dimY)*k + (i)*dimY + (j1)] + U[(dimX*dimY)*k + (i)*dimY + (j2)] + U[(dimX*dimY)*k1 + (i)*dimY + (j)] + U[(dimX*dimY)*k2 + (i)*dimY + (j)]; - sum *= lambda; - sum += mu*A[(dimX*dimY)*k + (i)*dimY + (j)]; - U[(dimX*dimY)*k + (i)*dimY + (j)] = normConst*sum; - }}} - return *U; + /* symmetric boundary conditions (Neuman) */ + i1 = i+1; if (i1 == dimX) i1 = i-1; + i2 = i-1; if (i2 < 0) i2 = i+1; + j1 = j+1; if (j1 == dimY) j1 = j-1; + j2 = j-1; if (j2 < 0) j2 = j+1; + k1 = k+1; if (k1 == dimZ) k1 = k-1; + k2 = k-1; if (k2 < 0) k2 = k+1; + + d_val = Dx[(dimX*dimY)*k + (i2)*dimY + (j)] - Dx[(dimX*dimY)*k + (i)*dimY + (j)] + Dy[(dimX*dimY)*k + (i)*dimY + (j2)] - Dy[(dimX*dimY)*k + (i)*dimY + (j)] + Dz[(dimX*dimY)*k2 + (i)*dimY + (j)] - Dz[(dimX*dimY)*k + (i)*dimY + (j)]; + b_val = -Bx[(dimX*dimY)*k + (i2)*dimY + (j)] + Bx[(dimX*dimY)*k + (i)*dimY + (j)] - By[(dimX*dimY)*k + (i)*dimY + (j2)] + By[(dimX*dimY)*k + (i)*dimY + (j)] - Bz[(dimX*dimY)*k2 + (i)*dimY + (j)] + Bz[(dimX*dimY)*k + (i)*dimY + (j)]; + sum = d_val + b_val; + sum += U[(dimX*dimY)*k + (i1)*dimY + (j)] + U[(dimX*dimY)*k + (i2)*dimY + (j)] + U[(dimX*dimY)*k + (i)*dimY + (j1)] + U[(dimX*dimY)*k + (i)*dimY + (j2)] + U[(dimX*dimY)*k1 + (i)*dimY + (j)] + U[(dimX*dimY)*k2 + (i)*dimY + (j)]; + sum *= lambda; + sum += mu*A[(dimX*dimY)*k + (i)*dimY + (j)]; + U[(dimX*dimY)*k + (i)*dimY + (j)] = normConst*sum; + }}} + return *U; } -float updDxDyDz_shrink3D(float *U, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ, float lambda) +float updDxDyDz_shrinkAniso3D(float *U, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ, float lambda) { - int i,j,i1,j1,k,k1; - float val1, val11, val2, val22, val3, val33; - - #pragma omp parallel for shared(U) private(i,j,i1,j1,k,k1,val1,val11,val2,val22,val3,val33) - for(i=0; i<dimX; i++) { + int i,j,i1,j1,k,k1,index; + float val1, val11, val2, val22, val3, val33, denom_lam; + denom_lam = 1.0f/lambda; +#pragma omp parallel for shared(U,denom_lam) private(index,i,j,i1,j1,k,k1,val1,val11,val2,val22,val3,val33) + for(i=0; i<dimX; i++) { for(j=0; j<dimY; j++) { for(k=0; k<dimZ; k++) { - /* symmetric boundary conditions (Neuman) */ - i1 = i+1; if (i1 == dimX) i1 = i-1; - j1 = j+1; if (j1 == dimY) j1 = j-1; - k1 = k+1; if (k1 == dimZ) k1 = k-1; - - val1 = (U[(dimX*dimY)*k + (i1)*dimY + (j)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) + Bx[(dimX*dimY)*k + (i)*dimY + (j)]; - val2 = (U[(dimX*dimY)*k + (i)*dimY + (j1)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) + By[(dimX*dimY)*k + (i)*dimY + (j)]; - val3 = (U[(dimX*dimY)*k1 + (i)*dimY + (j)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) + Bz[(dimX*dimY)*k + (i)*dimY + (j)]; - - val11 = fabs(val1) - 1.0f/lambda; if (val11 < 0) val11 = 0; - val22 = fabs(val2) - 1.0f/lambda; if (val22 < 0) val22 = 0; - val33 = fabs(val3) - 1.0f/lambda; if (val33 < 0) val33 = 0; - - if (val1 !=0) Dx[(dimX*dimY)*k + (i)*dimY + (j)] = (val1/fabs(val1))*val11; else Dx[(dimX*dimY)*k + (i)*dimY + (j)] = 0; - if (val2 !=0) Dy[(dimX*dimY)*k + (i)*dimY + (j)] = (val2/fabs(val2))*val22; else Dy[(dimX*dimY)*k + (i)*dimY + (j)] = 0; - if (val3 !=0) Dz[(dimX*dimY)*k + (i)*dimY + (j)] = (val3/fabs(val3))*val33; else Dz[(dimX*dimY)*k + (i)*dimY + (j)] = 0; - - }}} + index = (dimX*dimY)*k + (i)*dimY + (j); + /* symmetric boundary conditions (Neuman) */ + i1 = i+1; if (i1 == dimX) i1 = i-1; + j1 = j+1; if (j1 == dimY) j1 = j-1; + k1 = k+1; if (k1 == dimZ) k1 = k-1; + + val1 = (U[(dimX*dimY)*k + (i1)*dimY + (j)] - U[index]) + Bx[index]; + val2 = (U[(dimX*dimY)*k + (i)*dimY + (j1)] - U[index]) + By[index]; + val3 = (U[(dimX*dimY)*k1 + (i)*dimY + (j)] - U[index]) + Bz[index]; + + val11 = fabs(val1) - denom_lam; if (val11 < 0) val11 = 0; + val22 = fabs(val2) - denom_lam; if (val22 < 0) val22 = 0; + val33 = fabs(val3) - denom_lam; if (val33 < 0) val33 = 0; + + if (val1 !=0) Dx[index] = (val1/fabs(val1))*val11; else Dx[index] = 0; + if (val2 !=0) Dy[index] = (val2/fabs(val2))*val22; else Dy[index] = 0; + if (val3 !=0) Dz[index] = (val3/fabs(val3))*val33; else Dz[index] = 0; + + }}} + return 1; +} +float updDxDyDz_shrinkIso3D(float *U, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ, float lambda) +{ + int i,j,i1,j1,k,k1,index; + float val1, val11, val2, val3, denom, denom_lam; + denom_lam = 1.0f/lambda; +#pragma omp parallel for shared(U,denom_lam) private(index,denom,i,j,i1,j1,k,k1,val1,val11,val2,val3) + for(i=0; i<dimX; i++) { + for(j=0; j<dimY; j++) { + for(k=0; k<dimZ; k++) { + index = (dimX*dimY)*k + (i)*dimY + (j); + /* symmetric boundary conditions (Neuman) */ + i1 = i+1; if (i1 == dimX) i1 = i-1; + j1 = j+1; if (j1 == dimY) j1 = j-1; + k1 = k+1; if (k1 == dimZ) k1 = k-1; + + val1 = (U[(dimX*dimY)*k + (i1)*dimY + (j)] - U[index]) + Bx[index]; + val2 = (U[(dimX*dimY)*k + (i)*dimY + (j1)] - U[index]) + By[index]; + val3 = (U[(dimX*dimY)*k1 + (i)*dimY + (j)] - U[index]) + Bz[index]; + + denom = sqrt(val1*val1 + val2*val2 + val3*val3); + + val11 = (denom - denom_lam); if (val11 < 0) val11 = 0.0f; + + if (denom != 0.0f) { + Dx[index] = val11*(val1/denom); + Dy[index] = val11*(val2/denom); + Dz[index] = val11*(val3/denom); + } + else { + Dx[index] = 0; + Dy[index] = 0; + Dz[index] = 0; + } + }}} return 1; } float updBxByBz3D(float *U, float *Dx, float *Dy, float *Dz, float *Bx, float *By, float *Bz, int dimX, int dimY, int dimZ) { - int i,j,k,i1,j1,k1; - #pragma omp parallel for shared(U) private(i,j,k,i1,j1,k1) - for(i=0; i<dimX; i++) { + int i,j,k,i1,j1,k1; +#pragma omp parallel for shared(U) private(i,j,k,i1,j1,k1) + for(i=0; i<dimX; i++) { for(j=0; j<dimY; j++) { for(k=0; k<dimZ; k++) { - /* symmetric boundary conditions (Neuman) */ - i1 = i+1; if (i1 == dimX) i1 = i-1; - j1 = j+1; if (j1 == dimY) j1 = j-1; - k1 = k+1; if (k1 == dimZ) k1 = k-1; - - Bx[(dimX*dimY)*k + (i)*dimY + (j)] = Bx[(dimX*dimY)*k + (i)*dimY + (j)] + ((U[(dimX*dimY)*k + (i1)*dimY + (j)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) - Dx[(dimX*dimY)*k + (i)*dimY + (j)]); - By[(dimX*dimY)*k + (i)*dimY + (j)] = By[(dimX*dimY)*k + (i)*dimY + (j)] + ((U[(dimX*dimY)*k + (i)*dimY + (j1)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) - Dy[(dimX*dimY)*k + (i)*dimY + (j)]); - Bz[(dimX*dimY)*k + (i)*dimY + (j)] = Bz[(dimX*dimY)*k + (i)*dimY + (j)] + ((U[(dimX*dimY)*k1 + (i)*dimY + (j)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) - Dz[(dimX*dimY)*k + (i)*dimY + (j)]); - - }}} - return 1; + /* symmetric boundary conditions (Neuman) */ + i1 = i+1; if (i1 == dimX) i1 = i-1; + j1 = j+1; if (j1 == dimY) j1 = j-1; + k1 = k+1; if (k1 == dimZ) k1 = k-1; + + Bx[(dimX*dimY)*k + (i)*dimY + (j)] = Bx[(dimX*dimY)*k + (i)*dimY + (j)] + ((U[(dimX*dimY)*k + (i1)*dimY + (j)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) - Dx[(dimX*dimY)*k + (i)*dimY + (j)]); + By[(dimX*dimY)*k + (i)*dimY + (j)] = By[(dimX*dimY)*k + (i)*dimY + (j)] + ((U[(dimX*dimY)*k + (i)*dimY + (j1)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) - Dy[(dimX*dimY)*k + (i)*dimY + (j)]); + Bz[(dimX*dimY)*k + (i)*dimY + (j)] = Bz[(dimX*dimY)*k + (i)*dimY + (j)] + ((U[(dimX*dimY)*k1 + (i)*dimY + (j)] - U[(dimX*dimY)*k + (i)*dimY + (j)]) - Dz[(dimX*dimY)*k + (i)*dimY + (j)]); + + }}} + return 1; } /* General Functions */ /*****************************************************************/ diff --git a/main_func/compile_mex.m b/main_func/compile_mex.m index ea6e3a5..4d97bc2 100644 --- a/main_func/compile_mex.m +++ b/main_func/compile_mex.m @@ -1,4 +1,4 @@ % compile mex's mex LLT_model.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp" -mex FISTA_TV.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp" -mex SplitBregman_TV.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp"
\ No newline at end of file +mex FGP_TV.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp" +mex SplitBregman_TV.c CFLAGS="\$CFLAGS -fopenmp -Wall -std=c99" LDFLAGS="\$LDFLAGS -fopenmp" diff --git a/main_func/studentst.m b/main_func/studentst.m index 99fed1e..93e0a0a 100644 --- a/main_func/studentst.m +++ b/main_func/studentst.m @@ -1,47 +1,47 @@ -function [f,g,h,s,k] = studentst(r,k,s) -% Students T penalty with 'auto-tuning' -% -% use: -% [f,g,h,{k,{s}}] = studentst(r) - automatically fits s and k -% [f,g,h,{k,{s}}] = studentst(r,k) - automatically fits s -% [f,g,h,{k,{s}}] = studentst(r,k,s) - use given s and k -% -% input: -% r - residual as column vector -% s - scale (optional) -% k - degrees of freedom (optional) -% -% output: -% f - misfit (scalar) -% g - gradient (column vector) -% h - positive approximation of the Hessian (column vector, Hessian is a diagonal matrix) -% s,k - scale and degrees of freedom -% -% Tristan van Leeuwen, 2012. -% tleeuwen@eos.ubc.ca - -% fit both s and k -if nargin == 1 - opts = optimset('maxFunEvals',1e2); - tmp = fminsearch(@(x)st(r,x(1),x(2)),[1;2],opts); - s = tmp(1); - k = tmp(2); -end - - -if nargin == 2 - opts = optimset('maxFunEvals',1e2); - tmp = fminsearch(@(x)st(r,x,k),[1],opts); - s = tmp(1); -end - -% evaulate penalty -[f,g,h] = st(r,s,k); - - -function [f,g,h] = st(r,s,k) -n = length(r); -c = -n*(gammaln((k+1)/2) - gammaln(k/2) - .5*log(pi*s*k)); -f = c + .5*(k+1)*sum(log(1 + conj(r).*r/(s*k))); -g = (k+1)*r./(s*k + conj(r).*r); -h = (k+1)./(s*k + conj(r).*r); +function [f,g,h,s,k] = studentst(r,k,s)
+% Students T penalty with 'auto-tuning'
+%
+% use:
+% [f,g,h,{k,{s}}] = studentst(r) - automatically fits s and k
+% [f,g,h,{k,{s}}] = studentst(r,k) - automatically fits s
+% [f,g,h,{k,{s}}] = studentst(r,k,s) - use given s and k
+%
+% input:
+% r - residual as column vector
+% s - scale (optional)
+% k - degrees of freedom (optional)
+%
+% output:
+% f - misfit (scalar)
+% g - gradient (column vector)
+% h - positive approximation of the Hessian (column vector, Hessian is a diagonal matrix)
+% s,k - scale and degrees of freedom
+%
+% Tristan van Leeuwen, 2012.
+% tleeuwen@eos.ubc.ca
+
+% fit both s and k
+if nargin == 1
+ opts = optimset('maxFunEvals',1e2);
+ tmp = fminsearch(@(x)st(r,x(1),x(2)),[1;2],opts);
+ s = tmp(1);
+ k = tmp(2);
+end
+
+
+if nargin == 2
+ opts = optimset('maxFunEvals',1e2);
+ tmp = fminsearch(@(x)st(r,x,k),[1],opts);
+ s = tmp(1);
+end
+
+% evaulate penalty
+[f,g,h] = st(r,s,k);
+
+
+function [f,g,h] = st(r,s,k)
+n = length(r);
+c = -n*(gammaln((k+1)/2) - gammaln(k/2) - .5*log(pi*s*k));
+f = c + .5*(k+1)*sum(log(1 + conj(r).*r/(s*k)));
+g = (k+1)*r./(s*k + conj(r).*r);
+h = (k+1)./(s*k + conj(r).*r);
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