source/libtomo/recon/ospml_quad.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
// Laboratory (ANL), which is operated by UChicago Argonne, LLC for the
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#include "libtomo/recon.h"
#include "utils.h"
void
ospml_quad(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, int num_block, const int* ind_block)
{
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));
assert(coordx != NULL && coordy != NULL && ax != NULL && ay != NULL && by != NULL &&
bx != NULL && coorx != NULL && coory != NULL && dist != NULL && indi != NULL);
int s, q, p, d, i, m, n, os;
int quadrant;
float theta_p, sin_p, cos_p;
float mov, xi, yi;
int asize, bsize, csize;
float* simdata;
float upd;
int ind_data, ind_recon;
float* sum_dist;
float sum_dist2;
float *E, *F, *G;
int ind0, ind1, indg[8];
float totalwg, wg[8], mg[8];
const int blocksize = dt / num_block;
const int remainder = dt % num_block;
for(i = 0; i < num_iter; i++)
{
simdata = (float*) calloc((dt * dy * dx), sizeof(float));
// For each slice
for(s = 0; s < dy; s++)
{
preprocessing(ngridx, ngridy, dx, center[s], &mov, gridx,
gridy); // Outputs: mov, gridx, gridy
// For each ordered-subset num_subset
int subset_end = 0;
for(os = 0; os < num_block; os++)
{
const int subset_start = subset_end;
subset_end = subset_start + blocksize + ((os < remainder) ? 1 : 0);
assert(subset_end < dt);
sum_dist = (float*) calloc((ngridx * ngridy), sizeof(float));
E = (float*) calloc((ngridx * ngridy), sizeof(float));
F = (float*) calloc((ngridx * ngridy), sizeof(float));
G = (float*) calloc((ngridx * ngridy), sizeof(float));
// For each projection angle
for(int q = subset_start; q < subset_end; q++)
{
const int p = (num_block == 1) ? q : ind_block[q];
// 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
// 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];
}
// Update
if(sum_dist2 != 0.0f)
{
ind_data = d + p * dx + s * dt * dx;
ind_recon = s * ngridx * ngridy;
upd = data[ind_data] / simdata[ind_data];
for(n = 0; n < csize - 1; n++)
{
E[indi[n]] -= recon[indi[n] + ind_recon] * upd * dist[n];
}
}
}
}
// Weights for inner neighborhoods.
totalwg = 4 + 4 / sqrt(2);
wg[0] = 1 / totalwg;
wg[1] = 1 / totalwg;
wg[2] = 1 / totalwg;
wg[3] = 1 / totalwg;
wg[4] = 1 / sqrt(2) / totalwg;
wg[5] = 1 / sqrt(2) / totalwg;
wg[6] = 1 / sqrt(2) / totalwg;
wg[7] = 1 / sqrt(2) / totalwg;
// (inner region)
for(n = 1; n < ngridx - 1; n++)
{
for(m = 1; m < ngridy - 1; m++)
{
ind0 = m + n * ngridy;
ind1 = ind0 + s * ngridx * ngridy;
indg[0] = ind1 + 1;
indg[1] = ind1 - 1;
indg[2] = ind1 + ngridy;
indg[3] = ind1 - ngridy;
indg[4] = ind1 + ngridy + 1;
indg[5] = ind1 + ngridy - 1;
indg[6] = ind1 - ngridy + 1;
indg[7] = ind1 - ngridy - 1;
for(q = 0; q < 8; q++)
{
mg[q] = recon[ind1] + recon[indg[q]];
F[ind0] += 2 * reg_pars[0] * wg[q];
G[ind0] -= 2 * reg_pars[0] * wg[q] * mg[q];
}
}
}
// Weights for edges.
totalwg = 3 + 2 / sqrt(2);
wg[0] = 1 / totalwg;
wg[1] = 1 / totalwg;
wg[2] = 1 / totalwg;
wg[3] = 1 / sqrt(2) / totalwg;
wg[4] = 1 / sqrt(2) / totalwg;
// (top)
for(m = 1; m < ngridy - 1; m++)
{
ind0 = m;
ind1 = ind0 + s * ngridx * ngridy;
indg[0] = ind1 + 1;
indg[1] = ind1 - 1;
indg[2] = ind1 + ngridy;
indg[3] = ind1 + ngridy + 1;
indg[4] = ind1 + ngridy - 1;
for(q = 0; q < 5; q++)
{
mg[q] = recon[ind1] + recon[indg[q]];
F[ind0] += 2 * reg_pars[0] * wg[q];
G[ind0] -= 2 * reg_pars[0] * wg[q] * mg[q];
}
}
// (bottom)
for(m = 1; m < ngridy - 1; m++)
{
ind0 = m + (ngridx - 1) * ngridy;
ind1 = ind0 + s * ngridx * ngridy;
indg[0] = ind1 + 1;
indg[1] = ind1 - 1;
indg[2] = ind1 - ngridy;
indg[3] = ind1 - ngridy + 1;
indg[4] = ind1 - ngridy - 1;
for(q = 0; q < 5; q++)
{
mg[q] = recon[ind1] + recon[indg[q]];
F[ind0] += 2 * reg_pars[0] * wg[q];
G[ind0] -= 2 * reg_pars[0] * wg[q] * mg[q];
}
}
// (left)
for(n = 1; n < ngridx - 1; n++)
{
ind0 = n * ngridy;
ind1 = ind0 + s * ngridx * ngridy;
indg[0] = ind1 + 1;
indg[1] = ind1 + ngridy;
indg[2] = ind1 - ngridy;
indg[3] = ind1 + ngridy + 1;
indg[4] = ind1 - ngridy + 1;
for(q = 0; q < 5; q++)
{
mg[q] = recon[ind1] + recon[indg[q]];
F[ind0] += 2 * reg_pars[0] * wg[q];
G[ind0] -= 2 * reg_pars[0] * wg[q] * mg[q];
}
}
// (right)
for(n = 1; n < ngridx - 1; n++)
{
ind0 = (ngridy - 1) + n * ngridy;
ind1 = ind0 + s * ngridx * ngridy;
indg[0] = ind1 - 1;
indg[1] = ind1 + ngridy;
indg[2] = ind1 - ngridy;
indg[3] = ind1 + ngridy - 1;
indg[4] = ind1 - ngridy - 1;
for(q = 0; q < 5; q++)
{
mg[q] = recon[ind1] + recon[indg[q]];
F[ind0] += 2 * reg_pars[0] * wg[q];
G[ind0] -= 2 * reg_pars[0] * wg[q] * mg[q];
}
}
// Weights for corners.
totalwg = 2 + 1 / sqrt(2);
wg[0] = 1 / totalwg;
wg[1] = 1 / totalwg;
wg[2] = 1 / sqrt(2) / totalwg;
// (top-left)
ind0 = 0;
ind1 = ind0 + s * ngridx * ngridy;
indg[0] = ind1 + 1;
indg[1] = ind1 + ngridy;
indg[2] = ind1 + ngridy + 1;
for(q = 0; q < 3; q++)
{
mg[q] = recon[ind1] + recon[indg[q]];
F[ind0] += 2 * reg_pars[0] * wg[q];
G[ind0] -= 2 * reg_pars[0] * wg[q] * mg[q];
}
// (top-right)
ind0 = (ngridy - 1);
ind1 = ind0 + s * ngridx * ngridy;
indg[0] = ind1 - 1;
indg[1] = ind1 + ngridy;
indg[2] = ind1 + ngridy - 1;
for(q = 0; q < 3; q++)
{
mg[q] = recon[ind1] + recon[indg[q]];
F[ind0] += 2 * reg_pars[0] * wg[q];
G[ind0] -= 2 * reg_pars[0] * wg[q] * mg[q];
}
// (bottom-left)
ind0 = (ngridx - 1) * ngridy;
ind1 = ind0 + s * ngridx * ngridy;
indg[0] = ind1 + 1;
indg[1] = ind1 - ngridy;
indg[2] = ind1 - ngridy + 1;
for(q = 0; q < 3; q++)
{
mg[q] = recon[ind1] + recon[indg[q]];
F[ind0] += 2 * reg_pars[0] * wg[q];
G[ind0] -= 2 * reg_pars[0] * wg[q] * mg[q];
}
// (bottom-right)
ind0 = (ngridy - 1) + (ngridx - 1) * ngridy;
ind1 = ind0 + s * ngridx * ngridy;
indg[0] = ind1 - 1;
indg[1] = ind1 - ngridy;
indg[2] = ind1 - ngridy - 1;
for(q = 0; q < 3; q++)
{
mg[q] = recon[ind1] + recon[indg[q]];
F[ind0] += 2 * reg_pars[0] * wg[q];
G[ind0] -= 2 * reg_pars[0] * wg[q] * mg[q];
}
q = 0;
for(n = 0; n < ngridx * ngridy; n++)
{
G[q] += sum_dist[n];
q++;
}
for(n = 0; n < ngridx; n++)
{
for(m = 0; m < ngridy; m++)
{
q = m + n * ngridy;
if(F[q] != 0.0)
{
ind0 = q + s * ngridx * ngridy;
recon[ind0] = (-G[q] + sqrt(G[q] * G[q] - 8 * E[q] * F[q])) /
(4 * F[q]);
}
}
}
free(sum_dist);
free(E);
free(F);
free(G);
}
}
free(simdata);
}
free(gridx);
free(gridy);
free(coordx);
free(coordy);
free(ax);
free(ay);
free(bx);
free(by);
free(coorx);
free(coory);
free(dist);
free(indi);
}