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/*
* This work is part of the Core Imaging Library developed by
* Visual Analytics and Imaging System Group of the Science Technology
* Facilities Council, STFC
*
* Copyright 2019 Daniil Kazantsev
* Copyright 2019 Srikanth Nagella, Edoardo Pasca
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include "PD_TV_core.h"
/* C-OMP implementation of Primal-Dual TV [1] by Chambolle Pock denoising/regularization model (2D/3D case)
*
* Input Parameters:
* 1. Noisy image/volume
* 2. lambdaPar - regularization parameter
* 3. Number of iterations
* 4. eplsilon: tolerance constant
* 5. lipschitz_const: convergence related parameter
* 6. TV-type: methodTV - 'iso' (0) or 'l1' (1)
* 7. nonneg: 'nonnegativity (0 is OFF by default, 1 is ON)
* 8. tau: time marching parameter
* Output:
* [1] TV - Filtered/regularized image/volume
* [2] Information vector which contains [iteration no., reached tolerance]
*
* [1] Antonin Chambolle, Thomas Pock. "A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging", 2010
*/
float PDTV_CPU_main(float *Input, float *U, float *infovector, float lambdaPar, int iterationsNumb, float epsil, float lipschitz_const, int methodTV, int nonneg, float tau, int dimX, int dimY, int dimZ)
{
int ll;
long j, DimTotal;
float re, re1, sigma, theta, lt;
re = 0.0f; re1 = 0.0f;
int count = 0;
//tau = 1.0/powf(lipschitz_const,0.5);
//sigma = 1.0/powf(lipschitz_const,0.5);
sigma = 1.0/(lipschitz_const*tau);
theta = 1.0f;
lt = tau/lambdaPar;
ll = 0;
DimTotal = (long)(dimX*dimY*dimZ);
copyIm(Input, U, (long)(dimX), (long)(dimY), (long)(dimZ));
if (dimZ <= 1) {
/*2D case */
float *U_old=NULL, *P1=NULL, *P2=NULL;
U_old = calloc(DimTotal, sizeof(float));
P1 = calloc(DimTotal, sizeof(float));
P2 = calloc(DimTotal, sizeof(float));
/* begin iterations */
for(ll=0; ll<iterationsNumb; ll++) {
/* computing the the dual P variable */
DualP2D(U, P1, P2, (long)(dimX), (long)(dimY), sigma);
/* apply nonnegativity */
if (nonneg == 1) for(j=0; j<DimTotal; j++) {if (U[j] < 0.0f) U[j] = 0.0f;}
/* projection step */
Proj_func2D(P1, P2, methodTV, DimTotal);
/* copy U to U_old */
copyIm(U, U_old, (long)(dimX), (long)(dimY), 1l);
/* calculate divergence */
DivProj2D(U, Input, P1, P2,(long)(dimX), (long)(dimY), lt, tau);
/* check early stopping criteria */
if ((epsil != 0.0f) && (ll % 5 == 0)) {
re = 0.0f; re1 = 0.0f;
for(j=0; j<DimTotal; j++)
{
re += powf(U[j] - U_old[j],2);
re1 += powf(U[j],2);
}
re = sqrtf(re)/sqrtf(re1);
if (re < epsil) count++;
if (count > 3) break;
}
/*get updated solution*/
getX(U, U_old, theta, DimTotal);
}
free(P1); free(P2); free(U_old);
}
else {
/*3D case*/
float *U_old=NULL, *P1=NULL, *P2=NULL, *P3=NULL;
U_old = calloc(DimTotal, sizeof(float));
P1 = calloc(DimTotal, sizeof(float));
P2 = calloc(DimTotal, sizeof(float));
P3 = calloc(DimTotal, sizeof(float));
/* begin iterations */
for(ll=0; ll<iterationsNumb; ll++) {
/* computing the the dual P variable */
DualP3D(U, P1, P2, P3, (long)(dimX), (long)(dimY), (long)(dimZ), sigma);
/* apply nonnegativity */
if (nonneg == 1) for(j=0; j<DimTotal; j++) {if (U[j] < 0.0f) U[j] = 0.0f;}
/* projection step */
Proj_func3D(P1, P2, P3, methodTV, DimTotal);
/* copy U to U_old */
copyIm(U, U_old, (long)(dimX), (long)(dimY), (long)(dimZ));
DivProj3D(U, Input, P1, P2, P3, (long)(dimX), (long)(dimY), (long)(dimZ), lt, tau);
/* check early stopping criteria */
if ((epsil != 0.0f) && (ll % 5 == 0)) {
re = 0.0f; re1 = 0.0f;
for(j=0; j<DimTotal; j++)
{
re += powf(U[j] - U_old[j],2);
re1 += powf(U[j],2);
}
re = sqrtf(re)/sqrtf(re1);
if (re < epsil) count++;
if (count > 3) break;
}
/*get updated solution*/
getX(U, U_old, theta, DimTotal);
}
free(P1); free(P2); free(P3); free(U_old);
}
/*adding info into info_vector */
infovector[0] = (float)(ll); /*iterations number (if stopped earlier based on tolerance)*/
infovector[1] = re; /* reached tolerance */
return 0;
}
/*****************************************************************/
/************************2D-case related Functions */
/*****************************************************************/
/*Calculating dual variable (using forward differences)*/
float DualP2D(float *U, float *P1, float *P2, long dimX, long dimY, float sigma)
{
long i,j,index;
#pragma omp parallel for shared(U,P1,P2) private(index,i,j)
for(j=0; j<dimY; j++) {
for(i=0; i<dimX; i++) {
index = j*dimX+i;
/* symmetric boundary conditions (Neuman) */
if (i == dimX-1) P1[index] += sigma*(U[j*dimX+(i-1)] - U[index]);
else P1[index] += sigma*(U[j*dimX+(i+1)] - U[index]);
if (j == dimY-1) P2[index] += sigma*(U[(j-1)*dimX+i] - U[index]);
else P2[index] += sigma*(U[(j+1)*dimX+i] - U[index]);
}}
return 1;
}
/* Divergence for P dual */
float DivProj2D(float *U, float *Input, float *P1, float *P2, long dimX, long dimY, float lt, float tau)
{
long i,j,index;
float P_v1, P_v2, div_var;
#pragma omp parallel for shared(U,Input,P1,P2) private(index, i, j, P_v1, P_v2, div_var)
for(j=0; j<dimY; j++) {
for(i=0; i<dimX; i++) {
index = j*dimX+i;
/* symmetric boundary conditions (Neuman) */
if (i == 0) P_v1 = -P1[index];
else P_v1 = -(P1[index] - P1[j*dimX+(i-1)]);
if (j == 0) P_v2 = -P2[index];
else P_v2 = -(P2[index] - P2[(j-1)*dimX+i]);
div_var = P_v1 + P_v2;
U[index] = (U[index] - tau*div_var + lt*Input[index])/(1.0 + lt);
}}
return *U;
}
/*get the updated solution*/
float getX(float *U, float *U_old, float theta, long DimTotal)
{
long i;
#pragma omp parallel for shared(U,U_old) private(i)
for(i=0; i<DimTotal; i++) {
U[i] += theta*(U[i] - U_old[i]);
}
return *U;
}
/*****************************************************************/
/************************3D-case related Functions */
/*****************************************************************/
/*Calculating dual variable (using forward differences)*/
float DualP3D(float *U, float *P1, float *P2, float *P3, long dimX, long dimY, long dimZ, float sigma)
{
long i,j,k,index;
#pragma omp parallel for shared(U,P1,P2,P3) private(index,i,j,k)
for(k=0; k<dimZ; k++) {
for(j=0; j<dimY; j++) {
for(i=0; i<dimX; i++) {
index = (dimX*dimY)*k + j*dimX+i;
/* symmetric boundary conditions (Neuman) */
if (i == dimX-1) P1[index] += sigma*(U[(dimX*dimY)*k + j*dimX+(i-1)] - U[index]);
else P1[index] += sigma*(U[(dimX*dimY)*k + j*dimX+(i+1)] - U[index]);
if (j == dimY-1) P2[index] += sigma*(U[(dimX*dimY)*k + (j-1)*dimX+i] - U[index]);
else P2[index] += sigma*(U[(dimX*dimY)*k + (j+1)*dimX+i] - U[index]);
if (k == dimZ-1) P3[index] += sigma*(U[(dimX*dimY)*(k-1) + j*dimX+i] - U[index]);
else P3[index] += sigma*(U[(dimX*dimY)*(k+1) + j*dimX+i] - U[index]);
}}}
return 1;
}
/* Divergence for P dual */
float DivProj3D(float *U, float *Input, float *P1, float *P2, float *P3, long dimX, long dimY, long dimZ, float lt, float tau)
{
long i,j,k,index;
float P_v1, P_v2, P_v3, div_var;
#pragma omp parallel for shared(U,Input,P1,P2) private(index, i, j, k, P_v1, P_v2, P_v3, div_var)
for(k=0; k<dimZ; k++) {
for(j=0; j<dimY; j++) {
for(i=0; i<dimX; i++) {
index = (dimX*dimY)*k + j*dimX+i;
/* symmetric boundary conditions (Neuman) */
if (i == 0) P_v1 = -P1[index];
else P_v1 = -(P1[index] - P1[(dimX*dimY)*k + j*dimX+(i-1)]);
if (j == 0) P_v2 = -P2[index];
else P_v2 = -(P2[index] - P2[(dimX*dimY)*k + (j-1)*dimX+i]);
if (k == 0) P_v3 = -P3[index];
else P_v3 = -(P3[index] - P3[(dimX*dimY)*(k-1) + j*dimX+i]);
div_var = P_v1 + P_v2 + P_v3;
U[index] = (U[index] - tau*div_var + lt*Input[index])/(1.0 + lt);
}}}
return *U;
}
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