source/libtomo/recon/tv.c
// Copyright (c) 2015, UChicago Argonne, LLC. All rights reserved.
// Copyright 2015. UChicago Argonne, LLC. This software was produced
// under U.S. Government contract DE-AC02-06CH11357 for Argonne National
// Laboratongridx (ANL), which is operated by UChicago Argonne, LLC for the
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#include "libtomo/recon.h"
#include "utils.h"
#include "string.h"
void
tv(const float* data, int dy, int dt, int dx, const float* center, const float* theta,
float* recon, int ngridx, int ngridy, int num_iter, const float* reg_pars)
{
if(dy == 0 || dt == 0 || dx == 0)
return;
float* gridx = (float*) malloc((ngridx + 1) * sizeof(float));
float* gridy = (float*) malloc((ngridy + 1) * sizeof(float));
float* coordx = (float*) malloc((ngridy + 1) * sizeof(float));
float* coordy = (float*) malloc((ngridx + 1) * sizeof(float));
float* ax = (float*) malloc((ngridx + ngridy) * sizeof(float));
float* ay = (float*) malloc((ngridx + ngridy) * sizeof(float));
float* bx = (float*) malloc((ngridx + ngridy) * sizeof(float));
float* by = (float*) malloc((ngridx + ngridy) * sizeof(float));
float* coorx = (float*) malloc((ngridx + ngridy) * sizeof(float));
float* coory = (float*) malloc((ngridx + ngridy) * sizeof(float));
float* dist = (float*) malloc((ngridx + ngridy) * sizeof(float));
int* indi = (int*) malloc((ngridx + ngridy) * sizeof(int));
float* simdata = (float*) malloc((dy * dt * dx) * sizeof(float));
float* sum_dist = (float*) malloc((ngridx * ngridy) * sizeof(float));
float* update = (float*) malloc((dy * ngridx * ngridy) * sizeof(float));
float* prox0x = (float*) malloc((dy * ngridx * ngridy) * sizeof(float));
float* prox0y = (float*) malloc((dy * ngridx * ngridy) * sizeof(float));
float* prox1 = (float*) malloc((dy * dt * dx) * sizeof(float));
float* adjdata = (float*) malloc((dy * ngridx * ngridy) * sizeof(float));
assert(coordx != NULL && coordy != NULL && ax != NULL && ay != NULL && by != NULL &&
bx != NULL && coorx != NULL && coory != NULL && dist != NULL && indi != NULL &&
simdata != NULL && sum_dist != NULL && update != NULL);
int s, p, d, i, n;
int quadrant;
float theta_p, sin_p, cos_p;
float mov, xi, yi;
int asize, bsize, csize;
double upd;
int ind_data, ind_recon;
float sum_dist2;
int ix, iy;
// regularization parameters
float c;
float lambda;
// scaling constant r such that r*R(r*R^*(data)) ~ data
float r;
lambda = reg_pars[0];
c = 0.35;
r = 1 / sqrt(dx * dt / 2.0);
// scale initial guess
for(s = 0; s < dy; s++)
{
ind_recon = s * ngridx * ngridy;
for(iy = 0; iy < ngridy; iy++)
for(ix = 0; ix < ngridx; ix++)
recon[ind_recon + iy * ngridx + ix] /= r;
}
memcpy(update, recon, dy * ngridx * ngridy * sizeof(float));
memset(prox0x, 0, dy * ngridx * ngridy * sizeof(float));
memset(prox0y, 0, dy * ngridx * ngridy * sizeof(float));
memset(prox1, 0, dy * dt * dx * sizeof(float));
// Iterations
for(i = 0; i < num_iter; i++)
{
// initialize simdata to 0
memset(simdata, 0, dy * dt * dx * sizeof(float));
memset(adjdata, 0, dy * ngridx * ngridy * sizeof(float));
// For each slice
for(s = 0; s < dy; s++)
{
ind_recon = s * ngridx * ngridy;
// compute proximal of the gradient in x and y directions
// prox0 = prox0+c*grad(recon);
// prox0 = prox0/max(1,abs(prox0)/lambda);
for(iy = 0; iy < ngridy - 1; iy++)
for(ix = 0; ix < ngridx - 1; ix++)
{
prox0x[ind_recon + iy * ngridx + ix] +=
c * (recon[ind_recon + iy * ngridx + ix + 1] -
recon[ind_recon + iy * ngridx + ix]);
prox0y[ind_recon + iy * ngridx + ix] +=
c * (recon[ind_recon + (iy + 1) * ngridx + ix] -
recon[ind_recon + iy * ngridx + ix]);
}
for(iy = 0; iy < ngridy - 1; iy++)
for(ix = 0; ix < ngridx - 1; ix++)
{
upd = sqrt(prox0x[ind_recon + iy * ngridx + ix] *
prox0x[ind_recon + iy * ngridx + ix] +
prox0y[ind_recon + iy * ngridx + ix] *
prox0y[ind_recon + iy * ngridx + ix]) /
lambda;
upd = upd < 1 ? 1 : upd;
prox0x[ind_recon + iy * ngridx + ix] /= upd;
prox0y[ind_recon + iy * ngridx + ix] /= upd;
}
// compute proximal of the projections
// prox1 = 1*(prox1+c*R(recon)-c*data)/(1+c);
preprocessing(ngridx, ngridy, dx, center[s], &mov, gridx,
gridy); // Outputs: mov, gridx, gridy
// initialize sum_dist and update to zero
memset(sum_dist, 0, (ngridx * ngridy) * sizeof(float));
// For each projection angle
for(p = 0; p < dt; p++)
{
// Calculate the sin and cos values
// of the projection angle and find
// at which quadrant on the cartesian grid.
theta_p = fmodf(theta[p], 2.0f * (float) M_PI);
quadrant = calc_quadrant(theta_p);
sin_p = sinf(theta_p);
cos_p = cosf(theta_p);
// For each detector pixel
for(d = 0; d < dx; d++)
{
// Calculate coordinates
xi = -ngridx - ngridy;
yi = 0.5f * (1 - dx) + d + mov;
calc_coords(ngridx, ngridy, xi, yi, sin_p, cos_p, gridx, gridy,
coordx, coordy);
// Merge the (coordx, gridy) and (gridx, coordy)
trim_coords(ngridx, ngridy, coordx, coordy, gridx, gridy, &asize, ax,
ay, &bsize, bx, by);
// Sort the array of intersection points (ax, ay) and
// (bx, by). The new sorted intersection points are
// stored in (coorx, coory). Total number of points
// are csize.
sort_intersections(quadrant, asize, ax, ay, bsize, bx, by, &csize,
coorx, coory);
// Calculate the distances (dist) between the
// intersection points (coorx, coory). Find the
// indices of the pixels on the reconstruction grid.
calc_dist(ngridx, ngridy, csize, coorx, coory, indi, dist);
// Calculate simdata
calc_simdata(s, p, d, ngridx, ngridy, dt, dx, csize, indi, dist,
recon,
simdata); // Output: simdata
ind_data = d + p * dx + s * dt * dx;
prox1[ind_data] = (prox1[ind_data] + c * simdata[ind_data] * r -
c * data[ind_data]) /
(1 + c);
// Calculate dist*dist
sum_dist2 = 0.0f;
for(n = 0; n < csize - 1; n++)
{
sum_dist2 += dist[n] * dist[n];
sum_dist[indi[n]] += dist[n];
}
// adjoint Radon of the prox1 for further computations
// adjdata = R^*(prox1)
if(sum_dist2 != 0.0f)
for(n = 0; n < csize - 1; n++)
adjdata[ind_recon + indi[n]] += r * prox1[ind_data] * dist[n];
}
}
// copy recon = update
memcpy(&recon[ind_recon], &update[ind_recon],
ngridx * ngridy * sizeof(float));
// backward step. update with the divergence of prox0 and the
// adjoint of prox1 update = update-c*R^*(prox1)-c*div(prox0);
for(iy = 0; iy < ngridy; iy++)
for(ix = 0; ix < ngridx; ix++)
{
update[ind_recon + iy * ngridx + ix] -=
c * adjdata[ind_recon + iy * ngridx + ix];
if(ix == 0)
update[ind_recon + iy * ngridx + ix] +=
c * prox0x[ind_recon + iy * ngridx + ix];
else
update[ind_recon + iy * ngridx + ix] +=
c * (prox0x[ind_recon + iy * ngridx + ix] -
prox0x[ind_recon + iy * ngridx + ix - 1]);
if(iy == 0)
update[ind_recon + iy * ngridx + ix] +=
c * prox0y[ind_recon + iy * ngridx + ix];
else
update[ind_recon + iy * ngridx + ix] +=
c * (prox0y[ind_recon + iy * ngridx + ix] -
prox0y[ind_recon + (iy - 1) * ngridx + ix]);
}
// update of recon
// recon = 2*update - recon
for(iy = 0; iy < ngridy; iy++)
for(ix = 0; ix < ngridx; ix++)
recon[ind_recon + iy * ngridx + ix] =
2 * update[ind_recon + iy * ngridx + ix] -
recon[ind_recon + iy * ngridx + ix];
}
}
// scale result
for(s = 0; s < dy; s++)
{
ind_recon = s * ngridx * ngridy;
for(iy = 0; iy < ngridy; iy++)
for(ix = 0; ix < ngridx; ix++)
recon[ind_recon + iy * ngridx + ix] *= r;
}
free(gridx);
free(gridy);
free(coordx);
free(coordy);
free(ax);
free(ay);
free(bx);
free(by);
free(coorx);
free(coory);
free(dist);
free(indi);
free(simdata);
free(sum_dist);
free(update);
free(prox0x);
free(prox0y);
free(prox1);
free(adjdata);
}