source/libtomo/recon/grad.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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// * Redistributions of source code must retain the above copyright
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#include "libtomo/recon.h"
#include "utils.h"
#include "string.h"
void
grad(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* prox1 = (float*) malloc((dy * dt * dx) * sizeof(float));
float* grad = (float*) malloc((dy * ngridx * ngridy) * sizeof(float));
float* grad0 = (float*) malloc((dy * ngridx * ngridy) * sizeof(float));
float* recon0 = (float*) malloc((dy * ngridx * ngridy) * sizeof(float));
float* lambda = (float*) malloc((dy) * 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 && grad != NULL && grad0 != NULL &&
recon0 != NULL && lambda != 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;
// scaling constant r such that r*R(r*R^*(data)) ~ data
float r;
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;
}
memset(grad0, 0, dy * ngridx * ngridy * sizeof(float));
memset(prox1, 0, dy * dt * dx * sizeof(float));
memcpy(recon0, recon, dy * ngridx * ngridy * sizeof(float));
// Iterations
for(i = 0; i < num_iter; i++)
{
// initialize simdata and grad to 0
memset(simdata, 0, dy * dt * dx * sizeof(float));
memset(grad, 0, dy * ngridx * ngridy * sizeof(float));
// compute gradient, grad = 2*R^*(R(recon)-data)
// For each slice
for(s = 0; s < dy; s++)
{
ind_recon = s * ngridx * ngridy;
// compute proximal of the projections
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] = simdata[ind_data] * r - data[ind_data];
// 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];
}
if(sum_dist2 != 0.0f)
for(n = 0; n < csize - 1; n++)
grad[ind_recon + indi[n]] +=
2 * r * prox1[ind_data] * dist[n];
}
}
}
// compute the gradient step
for(s = 0; s < dy; s++)
{
if(reg_pars[0] < 0)
{
if(i == 0)
// first gradient step (small)
lambda[s] = 1e-3;
else
{
upd = 0;
lambda[s] = 0;
ind_recon = s * ngridx * ngridy;
for(iy = 0; iy < ngridy; iy++)
for(ix = 0; ix < ngridx; ix++)
{
lambda[s] += (recon[ind_recon + iy * ngridx + ix] -
recon0[ind_recon + iy * ngridx + ix]) *
(grad[ind_recon + iy * ngridx + ix] -
grad0[ind_recon + iy * ngridx + ix]);
upd += (grad[ind_recon + iy * ngridx + ix] -
grad0[ind_recon + iy * ngridx + ix]) *
(grad[ind_recon + iy * ngridx + ix] -
grad0[ind_recon + iy * ngridx + ix]);
}
lambda[s] /= upd;
}
}
else
lambda[s] = reg_pars[0];
}
// save previous iterations
memcpy(grad0, grad, dy * ngridx * ngridy * sizeof(float));
memcpy(recon0, recon, dy * ngridx * ngridy * sizeof(float));
// update, recon = recon - lambda*grad
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] -=
lambda[s] * grad[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(prox1);
free(recon0);
free(grad0);
free(grad);
}