% TOMO_SOLVER_DISTRIBUTED tomography solver that loads reconstruction from % ptychography, process them and use them to update the current tomgoraphy % reconstruction. Then create new estimates of ptychography objects % % volData = tomo_solver_distributed(par, volData, projData_rec, p0, theta_all, scan_ids) % % Inputs: % **par - parameter structure % **volData - initial guess of the tomographic volumes, values are linearized, ie projection = exp(sum(volData,1)) = prod(exp(volData),1) % **projData_rec - initial guess of the projections for each angle, probe, positions, etc % **p0 - basic parameters for the ptychography solver % **theta_all - all angles in degrees % **scan_ids - scan numbers that correspons to each angle value % *returns* % ++volData - final reconstruction of the tomographic volume % Academic License Agreement % % Source Code % % Introduction % • This license agreement sets forth the terms and conditions under which the PAUL SCHERRER INSTITUT (PSI), CH-5232 Villigen-PSI, Switzerland (hereafter "LICENSOR") % will grant you (hereafter "LICENSEE") a royalty-free, non-exclusive license for academic, non-commercial purposes only (hereafter "LICENSE") to use the PtychoShelves % computer software program and associated documentation furnished hereunder (hereafter "PROGRAM"). % % Terms and Conditions of the LICENSE % 1. LICENSOR grants to LICENSEE a royalty-free, non-exclusive license to use the PROGRAM for academic, non-commercial purposes, upon the terms and conditions % hereinafter set out and until termination of this license as set forth below. % 2. LICENSEE acknowledges that the PROGRAM is a research tool still in the development stage. The PROGRAM is provided without any related services, improvements % or warranties from LICENSOR and that the LICENSE is entered into in order to enable others to utilize the PROGRAM in their academic activities. It is the % LICENSEE’s responsibility to ensure its proper use and the correctness of the results.” % 3. THE PROGRAM IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR % A PARTICULAR PURPOSE AND NONINFRINGEMENT OF ANY PATENTS, COPYRIGHTS, TRADEMARKS OR OTHER RIGHTS. IN NO EVENT SHALL THE LICENSOR, THE AUTHORS OR THE COPYRIGHT % HOLDERS BE LIABLE FOR ANY CLAIM, DIRECT, INDIRECT OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY ARISING FROM, OUT OF OR IN CONNECTION WITH THE PROGRAM OR THE USE % OF THE PROGRAM OR OTHER DEALINGS IN THE PROGRAM. % 4. LICENSEE agrees that it will use the PROGRAM and any modifications, improvements, or derivatives of PROGRAM that LICENSEE may create (collectively, % "IMPROVEMENTS") solely for academic, non-commercial purposes and that any copy of PROGRAM or derivatives thereof shall be distributed only under the same % license as PROGRAM. The terms "academic, non-commercial", as used in this Agreement, mean academic or other scholarly research which (a) is not undertaken for % profit, or (b) is not intended to produce works, services, or data for commercial use, or (c) is neither conducted, nor funded, by a person or an entity engaged % in the commercial use, application or exploitation of works similar to the PROGRAM. % 5. LICENSEE agrees that it shall make the following acknowledgement in any publication resulting from the use of the PROGRAM or any translation of the code into % another computing language: % "Data processing was carried out using the PtychoShelves package developed by the Science IT and the coherent X-ray scattering (CXS) groups, Paul % Scherrer Institut, Switzerland." % % Additionally, any publication using the package, or any translation of the code into another computing language should cite % K. Wakonig, H.-C. Stadler, M. Odstrčil, E.H.R. Tsai, A. Diaz, M. Holler, I. Usov, J. Raabe, A. Menzel, M. Guizar-Sicairos, PtychoShelves, a versatile % high-level framework for high-performance analysis of ptychographic data, J. Appl. Cryst. 53(2) (2020). (doi: 10.1107/S1600576720001776) % and for difference map: % P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, High-resolution scanning X-ray diffraction microscopy, Science 321, 379–382 (2008). % (doi: 10.1126/science.1158573), % for maximum likelihood: % P. Thibault and M. Guizar-Sicairos, Maximum-likelihood refinement for coherent diffractive imaging, New J. Phys. 14, 063004 (2012). % (doi: 10.1088/1367-2630/14/6/063004), % for LSQ-ML: % M. Odstrčil, A. Menzel, and M. Guizar-Sicairos, Iterative least-squares solver for generalized maximum-likelihood ptychography, Opt. Express 26(3), 3108 (2018). % (doi: 10.1364/OE.26.003108), % for mixed coherent modes: % P. Thibault and A. Menzel, Reconstructing state mixtures from diffraction measurements, Nature 494, 68–71 (2013). (doi: 10.1038/nature11806), % and/or for multislice: % E. H. R. Tsai, I. Usov, A. Diaz, A. Menzel, and M. Guizar-Sicairos, X-ray ptychography with extended depth of field, Opt. Express 24, 29089–29108 (2016). % (doi: 10.1364/OE.24.029089), % and/or for OPRP: % M. Odstrcil, P. Baksh, S. A. Boden, R. Card, J. E. Chad, J. G. Frey, W. S. Brocklesby, Ptychographic coherent diffractive imaging with orthogonal probe relaxation. % Opt. Express 24.8 (8360-8369) 2016. (doi: 10.1364/OE.24.008360). % 6. Except for the above-mentioned acknowledgment, LICENSEE shall not use the PROGRAM title or the names or logos of LICENSOR, nor any adaptation thereof, nor the % names of any of its employees or laboratories, in any advertising, promotional or sales material without prior written consent obtained from LICENSOR in each case. % 7. Ownership of all rights, including copyright in the PROGRAM and in any material associated therewith, shall at all times remain with LICENSOR, and LICENSEE % agrees to preserve same. LICENSEE agrees not to use any portion of the PROGRAM or of any IMPROVEMENTS in any machine-readable form outside the PROGRAM, nor to % make any copies except for its internal use, without prior written consent of LICENSOR. LICENSEE agrees to place the following copyright notice on any such copies: % © All rights reserved. PAUL SCHERRER INSTITUT, Switzerland, Laboratory for Macromolecules and Bioimaging, 2017. % 8. The LICENSE shall not be construed to confer any rights upon LICENSEE by implication or otherwise except as specifically set forth herein. % 9. DISCLAIMER: LICENSEE shall be aware that Phase Focus Limited of Sheffield, UK has an international portfolio of patents and pending applications which relate % to ptychography and that the PROGRAM may be capable of being used in circumstances which may fall within the claims of one or more of the Phase Focus patents, % in particular of patent with international application number PCT/GB2005/001464. The LICENSOR explicitly declares not to indemnify the users of the software % in case Phase Focus or any other third party will open a legal action against the LICENSEE due to the use of the program. % 10. This Agreement shall be governed by the material laws of Switzerland and any dispute arising out of this Agreement or use of the PROGRAM shall be brought before % the courts of Zürich, Switzerland. function volData = tomo_solver_distributed(par, volData, projData_rec, p0, theta_all, scan_ids) import utils.* % be sure to clean GPU first reset(gpuDevice) p0.queue.path = par.queue_path; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%% create the queue %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% system(['rm -rf ', par.queue_path]); % if exist(par.queue_path, 'dir') % rmdir(par.queue_path, 's'); % end Nangles = length(theta_all); try; mkdir([par.queue_path, '/pending/']); end try; mkdir([par.queue_path, '/done/']); end system('rm temp/*/prepared_data.mat '); % minimum p structure needed to create the queue p_init.prepare_data_path = par.prepare_data_path; % create file queue for ii = 1:Nangles utils.progressbar(ii,length(scan_ids)); p = p_init; p.scan_number = scan_ids(ii); save('-v6',fullfile(par.queue_path, sprintf('pending/scan%05d.mat',scan_ids(ii))), 'p'); end initial_settings = 'p_initial.mat'; save(initial_settings, 'p0'); Npx_vol = size(volData); assert(Npx_vol(1)==Npx_vol(2), 'Horizontal volume size has to be symmetric') assert(mod(Npx_vol(1),64) == 0, 'Input volum esize should be dividable by 64') thickness = p0.thickness; % Total thickness of the simulated sample if multiple layers are provided; Nangles = length(projData_rec); % choosed optimally distributed the angles in the 180 deg range to minimize overlap angle_step = median(diff(theta_all)); init_angle = math.argmin(abs(theta_all - 180-angle_step*par.downsample_angles/2)); angle_indices = [1:par.downsample_angles:init_angle-1, init_angle:par.downsample_angles:Nangles]; volData_hist = {[],[]}; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % initialize one dataset [p0] = core.initialize_ptycho(p0); p0.prepare_data_path = par.prepare_data_path; gpu = gpuDevice(); %% create some loost support mask r if par.apply_support m_volData = abs(mean(volData,3)); support_mask = utils.imgaussfilt2_fft(m_volData, 20) > mean(m_volData(:))/2; support_mask = utils.imgaussfilt3_conv(support_mask, [10,10,0]); volData = volData .* support_mask; else support_mask = 1; end %% move arrays to GPU par.support_mask = Garray(support_mask); par.norm_full = norm(volData(:)); % move to uint8 - the volume has to be on GPU !! moving from and to GPU % causes too much overhead volData = ptychotomo.compress_volume(volData, par); volData = Garray(volData); % prepate support masks for the projections using the "support_mask" calculated from the % reconstructed tomography volume par.weight = sum(support_mask); par.weight = utils.crop_pad(par.weight, [1,p0.object_size(2)]); par.weight = 1-par.weight / max(par.weight); par.support_mask = support_mask; % store all volumes per iteration volData_all = cell(par.Niter,1); disp('Reconstructing') %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% iterativelly solve ptycho tomo task %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% update_norm = nan(par.Niter, Nangles, par.Niter_inner); fourier_error = nan(par.Niter, Nangles,2); update_norm_acc = nan(par.Niter, 1); hist_numbers = zeros(Nangles,1); ptycho_results = cell(Nangles,1); % store temporally data used for reconstruction , avoid data storing Npx_proj = [p0.object_size, 1]; proj_number_list = []; % list of projections yet in procesing t_plot = tic; for iter = 1:par.Niter if iter >= max(par.ptycho_reconstruct_start, par.ptycho_ML_reconstruct_start) Nlayers = min(2^ceil((iter+1 - par.ptycho_ML_reconstruct_start)), par.Nlayers_max ); else Nlayers = 1; end Npx_proj(3) = Nlayers; full_reconstruction = mod(iter,par.ptycho_interval) == 0 && iter >= par.ptycho_reconstruct_start; fprintf('Free GPU mem: %3.4gGB \n', gpu.AvailableMemory / 1e9) fprintf('Iteration %i/%i Nlayers %i full_reconstruction %i \n', iter, par.Niter, Nlayers, full_reconstruction) layer_distance = thickness / Nlayers * ones(1,Nlayers-1) ; Ngroups = length(angle_indices); group_ind = get_golden_ratio_groups(theta_all(angle_indices), Ngroups); %%%%% start accelerated gradients %%%%%%%%%%%%%% if iter == par.ptycho_accel_start volData_hist{1} = ptychotomo.decompress_volume(gather(volData), par); volData_hist{2} = volData_hist{1}; elseif iter > par.ptycho_accel_start beta = (iter-par.ptycho_accel_start+1)/(iter-par.ptycho_accel_start+3); volData_hist{1} = volData_hist{2}; volData_hist{2} = ptychotomo.decompress_volume(gather(volData), par); upd = beta*(volData_hist{1}- volData_hist{2}); update_norm_acc(iter) = norm(upd(:)); if ~isfinite(update_norm_acc(iter)) keyboard end if all(isfinite(update_norm_acc([iter, iter-1]))) && (update_norm_acc(iter) > update_norm_acc(iter-1)) % reset the accelerated gradients warning('Reset accelerated gradients') volData_hist{1} = ptychotomo.decompress_volume(gather(volData), par); volData_hist{2} = volData_hist{1}; par.ptycho_accel_start = iter; else % else move in the accelerated direction volData = volData_hist{2} + upd; end volData = ptychotomo.compress_volume(volData, par); volData = utils.Garray(volData); % move it back to GPU after gathering for acceleratin computation clear upd end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% verbose(struct('prefix', {'ptychotomo'})) for outer_loop = 1:par.Niter_inner fprintf('Outer loop %i \n', outer_loop) tic group_id = 1; while group_id <= Ngroups || ~isempty(proj_number_list) if verbose() < 0 utils.progressbar(group_id, Ngroups) end clear volData_upd_full verbose(0,'PREPARING') try %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%% prepare new initial guess if needed %%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% proj_number_list_update = []; while length(proj_number_list) < par.max_queue_length && group_id <= Ngroups ind = angle_indices(group_ind{group_id}); % calculate how the projection should look like and store the initial guess to "initial_guess.mat" for ll = 1:length(ind) proj_number = ind(ll); scan_number = scan_ids(proj_number); if ~isempty(dir(sprintf('%s/pending/scan%05i.mat', par.queue_path,scan_number))) verbose(0, 'Preparing %i', scan_number) verbose(0); [projData_model{proj_number}, projData_rec{proj_number}, ptycho_results{proj_number}] = ... ptychotomo.prepare_distributed_data(p0, volData, projData_rec{proj_number},layer_distance, par, ... iter == par.ptycho_reconstruct_start, iter >= par.ptycho_reconstruct_start ); if iter >= par.ptycho_reconstruct_start % file is ready for processing, move it to queue io.movefile_fast(sprintf('%s/pending/scan%05i.mat', par.queue_path,scan_number), sprintf('%s/scan%05i.mat', par.queue_path,scan_number)); else % skip ptychography reconstrution, pretent that the file is already finished io.movefile_fast(sprintf('%s/pending/scan%05i.mat', par.queue_path,scan_number), sprintf('%s/done/scan%05i.mat', par.queue_path,scan_number)); end hist_numbers(proj_number) = hist_numbers(proj_number) +1; proj_number_list_update(end+1) = proj_number; proj_number_list(end+1) = proj_number; continue else verbose(0, 'Waiting for scan %i to be returned to /pending/', scan_number) end end group_id = group_id + 1; end catch err keyboard end clear scan_number proj_number %%%%%%% run the reconstruction using the generated queue files %%% if iter < par.ptycho_reconstruct_start verbose(0,'TOMO RECONSTRUCTING') for proj_number = proj_number_list_update % save previous object estimation and pretend that they were just calculated proj = projData_rec{proj_number}; pout.object{1} = exp(proj.object_c); pout.probes = proj.probe; pout.positions = proj.positions; pout.asize = p0.asize; ferr = nan; ptycho_results{proj_number} = pout; end prepare_data_path = sprintf(p0.prepare_data_path, scan_ids(proj_number)); else verbose(0,'PTYCHOTOMO RECONSTRUCTING') end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% verbose(struct('prefix', {'ptychotomo'})) verbose(0,'GATHERING') %%%%%%%%%%%%%% apply the recent reconstructions into the 3D volume %%%%%% % load the stored reconstructions and return corresponding object update %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% start gathering reconstructions %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% volData_upd_full = 0; proj_number = proj_number_list(1); scan_number = scan_ids(proj_number); proj_number_list(1) = []; scan_file_path = sprintf('%s/done/scan%05d.mat', par.queue_path, scan_number); timeout_gathering = 0.1; % [s] ii = 0; while true verbose(0) if ii * timeout_gathering > par.wait_time_solver % skip projetions that were not delivered in more than % "wait_time_solver" time warning('Failed to gather %s', scan_file_path) break end if exist(scan_file_path, 'file') break else % wait for solver to prepare the reconstruction pause(timeout_gathering) if ii == 0; verbose(0,'Waiting for reconstruction %i', scan_number); end ii = ii + 1; continue end end if ii * timeout_gathering > par.wait_time_solver continue end p0.scan_number = scan_number; verbose(0) verbose(0, 'Gathering %i', p0.scan_number) if iter >= par.start_3D_reconstruction par.update_step = par.lambda/length(ind)/outer_loop; par.update_step = complex(par.update_step / 5, par.update_step); % much slower convergence for amplitude else par.update_step = 0; end try if ii * timeout_gathering < par.wait_time_solver % calculate and accumulate update of the 3D volume [volData,projData_rec{proj_number}, fourier_error(iter,proj_number,:), update_norm(iter,proj_number,outer_loop)] = ... ptychotomo.gather_distributed_reconstructions(volData, projData_model{proj_number}, ptycho_results{proj_number},par); end catch err warning('gather_distributed_reconstructions failed: %s', err.message) end % file is already used, move it back to pending ... io.movefile_fast(scan_file_path, sprintf('%s/pending/scan%05i.mat', par.queue_path,p0.scan_number)); % release shared memory if isa(ptycho_results{proj_number}, 'shm') ptycho_results{proj_number}.protected = false; % make it possible to delete the SHM ptycho_results{proj_number}.detach; ptycho_results{proj_number}.free() ; % free shared memory ptycho_results{proj_number} = []; end % save memory projData_model{proj_number}.object = gather(projData_model{proj_number}.object); projData_model{proj_number}.object_c = gather(projData_model{proj_number}.object_c); ptycho_results{proj_number} = []; if math.norm2(projData_rec{proj_number}.probe) > 2.1 keyboard end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %%%%%%%%%%% PLOT PROGRESS %%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if par.debug || toc(t_plot) > par.plot_every plotting.smart_figure(24) subplot(2,2,1) plotting.imagesc3D(-imag( ptychotomo.decompress_volume(volData(:,:,ceil(end/2)),par))); caxis(gather(math.sp_quantile(-imag(volData(:,:,100)), [5e-3, 1-5e-3], 10))) axis off image colormap bone title('Current reconstruction') subplot(2,2,2) ind_ok = find(any(~isnan(fourier_error(:,:,1)),2)); plot(ind_ok,fourier_error(ind_ok,:,1), '-') hold all plot(ind_ok,fourier_error(ind_ok,:,2), '--') plot(ind_ok,nanmean(fourier_error(ind_ok,:,1),2), 'k-', 'Linewidth', 2) plot(ind_ok,nanmean(fourier_error(ind_ok,:,2),2), 'k--', 'Linewidth', 2) hold off set(gca, 'xscale', 'log') set(gca, 'yscale', 'log') grid on axis tight title('Fourier error (from ptycho)') subplot(2,2,3) plot(update_norm(:,:,1)) hold all plot(update_norm_acc, 'k--', 'Linewidth', 2) plot(nanmean(update_norm(:,:,1),2), 'k', 'Linewidth', 2) plot(nanmean(update_norm(:,:,end),2), 'k:', 'Linewidth', 2) hold off set(gca, 'xscale', 'log') set(gca, 'yscale', 'log') grid on title('Update difference (in tomo)') axis tight subplot(2,2,4) plotting.imagesc3D(exp(crop_pad(sum(projData_rec{proj_number}.object_c,3), [Npx_vol(3), Npx_vol(1)]))) axis xy off image title('Example of a projection') %drawnow plotting.smart_figure(15222) subplot(2,2,1) plotting.imagesc3D(abs(exp(sum(projData_rec{proj_number}.object_c,3)))) colorbar colormap bone axis xy off image caxis([0.8, 1.1]) title('Ptycho - abs') subplot(2,2,2) plotting.imagesc3D(angle(exp(sum(projData_rec{proj_number}.object_c,3)))) colorbar colormap bone axis xy off image title('Model - phase') subplot(2,2,3) plotting.imagesc3D(abs(exp(sum(projData_model{proj_number}.object_c,3)))) colorbar colormap bone axis xy off image title('Model - abs') caxis([0.8, 1.1]) subplot(2,2,4) plotting.imagesc3D(angle(exp(sum(projData_model{proj_number}.object_c,3)))) colorbar colormap bone title('Model - phase') axis xy off image if par.Niter_inner > 1 plotting.smart_figure(13123) plot(squeeze(update_norm(max(1,iter-1),:,:))') hold all plot(nanmedian(squeeze(update_norm(max(1,iter-1),:,:)),1) ,'k','Linewidth', 2) hold off set(gca, 'xscale', 'log') set(gca, 'yscale', 'log') title(sprintf('Inner loop convergence iter = %i Nlayers = %i', iter, Nlayers)) axis tight end drawnow t_plot = tic; end end toc end try volData = ptychotomo.decompress_volume(volData, par); % plotting.smart_figure(123123) % subplot(1,2,1) % plotting.imagesc3D(log(mean(abs(math.fftshift_2D(fft2(exp(gather(volData))))),3))) % axis image off % colormap(plotting.colormaps.franzmap) % title('FFT of reconstruction') % subplot(1,2,2) % plotting.imagesc3D(log(mean(abs(math.fftshift_2D(fft2(exp(gather(volData_upd_full))))),3))) % axis image off % colormap(plotting.colormaps.franzmap) % title('FFT of last update') % suptitle(sprintf('Iter %i Nlayers %i fullrecons %i', iter, Nlayers, full_reconstruction)) %% plotting.smart_figure(234) frame = ceil(size(volData,3)/2); subplot(1,2,1) plotting.imagesc3D(-imag(volData(:,:,frame))); caxis(gather(math.sp_quantile(-imag(volData(:,:,frame)), [5e-3, 1-5e-3], 10))) axis off image colorbar colormap bone title('Phase') subplot(1,2,2) plotting.imagesc3D(-real(volData(:,:,frame))); caxis(gather(math.sp_quantile(-real(volData(:,:,frame)), [5e-3, 1-5e-3], 10))) colorbar axis off image colormap bone title('Absorbtion') plotting.suptitle(sprintf('Reconstruction in %i-th iteration', iter)) %% img = -gather(imag(volData(:,:,frame))); img = img / math.sp_quantile(img, 1-5e-3, 1); img = max(0, min(1, img)); if ~exist('./results_ptychotomo', 'dir'); mkdir('results_ptychotomo'); end imwrite(gray2ind(img), bone, sprintf('results_ptychotomo/img_3d_ptycho_iter%i_Nlayers_%i.png', iter, Nlayers)) if ~par.debug %% save a preview on disk % suptitle(sprintf('Iter %i Nlayers %i fullrecons %i', iter, Nlayers, full_reconstruction)) % print('-dpng', '-f234', '-r300', sprintf('results_ptychotomo/progress_3d_ptycho_iter%i_Nlayers_%i.png', iter, Nlayers)) end catch err warning('Plotting failed') keyboard end volData_all{iter} = gather(volData(:,:,ceil(end/2))); % save memory volData_upd_full = []; volData = ptychotomo.compress_volume(volData, par); end %% show final results for iter = 1:par.Niter-1 try volupd(:,:,iter) =volData_all{iter+1} - volData_all{iter}; volprev(:,:,iter) =volData_all{iter}; end end for iter = 1:par.Niter-2 try a = volupd(:,:,iter); b = volupd(:,:,iter+1); C(iter) = abs(corr(a(:), b(:))); end end figure subplot(1,2,1) plotting.imagesc3D(-imag(volprev)) colormap bone axis off image title('Phase') subplot(1,2,2) plotting.imagesc3D(-real(volprev)) colormap bone axis off image title('Absorbtion') plotting.suptitle('Reconstruction quality in each iteration') figure plotting.imagesc3D(volupd) axis off image title('Complex volume update in each iteration') end