Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
Add Tikhonov regularization with Identity Tikhonov matrix (#438)
* Add Tikhonov regularization with Identinity Tikhonov matrix * Fixing the test for Tikhonov regularization * Fixinig shape of the regularization data
- Loading branch information
Showing
9 changed files
with
310 additions
and
6 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,264 @@ | ||
| // 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 | ||
| // U.S. Department of Energy. The U.S. Government has rights to use, | ||
| // reproduce, and distribute this software. NEITHER THE GOVERNMENT NOR | ||
| // UChicago Argonne, LLC MAKES ANY WARRANTY, EXPRESS OR IMPLIED, OR | ||
| // ASSUMES ANY LIABILITY FOR THE USE OF THIS SOFTWARE. If software is | ||
| // modified to produce derivative works, such modified software should | ||
| // be clearly marked, so as not to confuse it with the version available | ||
| // from ANL. | ||
|
|
||
| // Additionally, redistribution and use in source and binangridx forms, with | ||
| // or without modification, are permitted provided that the following | ||
| // conditions are met: | ||
|
|
||
| // * Redistributions of source code must retain the above copyright | ||
| // notice, this list of conditions and the following disclaimer. | ||
|
|
||
| // * Redistributions in binangridx form must reproduce the above copyright | ||
| // notice, this list of conditions and the following disclaimer in | ||
| // the documentation and/or other materials provided with the | ||
| // distribution. | ||
|
|
||
| // * Neither the name of UChicago Argonne, LLC, Argonne National | ||
| // Laboratongridx, ANL, the U.S. Government, nor the names of its | ||
| // contributors may be used to endorse or promote products derived | ||
| // from this software without specific prior written permission. | ||
|
|
||
| // THIS SOFTWARE IS PROVIDED BY UChicago Argonne, LLC AND CONTRIBUTORS | ||
| // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | ||
| // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS | ||
| // FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL UChicago | ||
| // Argonne, LLC OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, | ||
| // INCIDENTAL, SPECIAL, EXEMPLAngridx, OR CONSEQUENTIAL DAMAGES (INCLUDING, | ||
| // BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | ||
| // LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER | ||
| // CAUSED AND ON ANY THEOngridx OF LIABILITY, WHETHER IN CONTRACT, STRICT | ||
| // LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN | ||
| // ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE | ||
| // POSSIBILITY OF SUCH DAMAGE. | ||
|
|
||
| #include "utils.h" | ||
|
|
||
| void | ||
| tikh(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_data, 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]; | ||
| } | ||
| } | ||
| } | ||
|
|
||
| // add to the gradient 2*reg_par[1]*(recon-reg_data) | ||
| for(s = 0; s < dy; s++) | ||
| { | ||
| ind_recon = s * ngridx * ngridy; | ||
| for(iy = 0; iy < ngridy; iy++) | ||
| for(ix = 0; ix < ngridx; ix++) | ||
| grad[ind_recon + iy * ngridx + ix] += 2*reg_pars[1]*(recon[ind_recon + iy * ngridx + ix]-reg_data[ind_recon + iy * ngridx + ix]); | ||
| } | ||
| // 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); | ||
| } |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Binary file not shown.
Oops, something went wrong.