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% [U,S,V,rec_all, rec_all_0] = SVD_regularization(sinogram, theta, Niter_SVD, Npix, reconstruct_ind,max_projections,par)
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% perform spectral SVD analysis and SART based reconstruction
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% Inputs:
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% sinogram - unwrapped sinogram
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% theta - projection angles
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% Niter_SVD - number of iteration of the SVD optimization
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% Npix - (3x1 int), size of the output volume
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% reconstruct_ind - (int array) list of angles that will be considered for reconstruction
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% max_projections - maximal number of projections selected for each
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% energy step. Set "inf" to ignore this limit. It is useful to
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% equialize the weight for each energy step when the distribution is
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% highly unequal
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% par - tomogrpahy paramter structure
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% Outputs:
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% U,S,V - SVD vectors
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% rec_all - regularized SART reconstructions for each energy
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% rec_all_0 - oriignal FBP reocnstructions before SVD regularization
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%*-----------------------------------------------------------------------*
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%| |
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%| Except where otherwise noted, this work is licensed under a |
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%| Creative Commons Attribution-NonCommercial-ShareAlike 4.0 |
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%| International (CC BY-NC-SA 4.0) license. |
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%| |
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%| Copyright (c) 2017 by Paul Scherrer Institute (http://www.psi.ch) |
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%| |
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%| Author: CXS group, PSI |
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%*-----------------------------------------------------------------------*
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% You may use this code with the following provisions:
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%
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% If the code is fully or partially redistributed, or rewritten in another
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% computing language this notice should be included in the redistribution.
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%
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% If this code, or subfunctions or parts of it, is used for research in a
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% publication or if it is fully or partially rewritten for another
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% computing language the authors and institution should be acknowledged
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% in written form in the publication: “Data processing was carried out
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% using the “cSAXS matlab package” developed by the CXS group,
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% Paul Scherrer Institut, Switzerland.”
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% Variations on the latter text can be incorporated upon discussion with
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% the CXS group if needed to more specifically reflect the use of the package
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% for the published work.
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%
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% A publication that focuses on describing features, or parameters, that
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% are already existing in the code should be first discussed with the
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% authors.
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%
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% This code and subroutines are part of a continuous development, they
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% are provided “as they are” without guarantees or liability on part
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% of PSI or the authors. It is the user responsibility to ensure its
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% proper use and the correctness of the results.
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function [U,S,V,rec_all, rec_all_0] = SVD_regularization(sinogram, theta, Niter_SVD, Npix, reconstruct_ind,max_projections,par)
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% internal parameters
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SART_grouping = 25;
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Niter_SART = 10;
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Nmodes = 2;
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Nangles = length(theta);
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E_all = unique(par.energy(ismember(1:Nangles, reconstruct_ind) ));
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Nenergy = length(E_all);
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tomogram_edensity = cell(Nenergy,1);
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for ii = 1:Nenergy
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utils.progressbar(ii,Nenergy)
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% choose projections to process
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rec_ind = find(par.energy == E_all(ii) & ismember(1:Nangles,reconstruct_ind)'); % use only some angles
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% downsample to the requested "max_projections"
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rec_ind = rec_ind(1:max(1,ceil(length(rec_ind)/max_projections)):end);
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num_proj_all(ii) = length(rec_ind);
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if isempty(rec_ind)
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tomogram_edensity{ii} = zeros(Npix,Npix,size(sinogram,1),'single');
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continue;
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end
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%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%
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[Nlayers,width_sinogram,~] = size(sinogram);
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CoR = [Nlayers,width_sinogram]/2; % there is 0.5px shift between fft_1d/fft_2d vs none
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[cfg, vectors] = astra.ASTRA_initialize([Npix,Npix, Nlayers],[Nlayers,width_sinogram],theta,par.lamino_angle,par.tilt_angle,1,CoR);
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% find optimal split of the dataset for given GPU
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split = astra.ASTRA_find_optimal_split(cfg, length(par.GPU_list), 1);
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% new FBP code
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tomogram = tomo.FBP_zsplit(sinogram, cfg, vectors, split,'valid_angles',rec_ind,...
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'determine_weights', true, ...
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'GPU', par.GPU_list,'filter',par.filter_type, 'filter_value',par.freq_scale, 'verbose',0);
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% Caclulate delta tomogram
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par.lambda = 1.234e-9 / E_all(ii);
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par.factor=par.lambda/(2*pi*par.pixel_size);
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par.factor_edensity = 1e-30*2*pi/(par.lambda^2*2.81794e-15);
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% get full reconstruction (for FBP is sum already final tomogram)
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% calculate complex refractive index
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tomogram_edensity{ii} = gather(tomogram*par.factor*par.factor_edensity);
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end
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% quantity = min(max_projections, hist(par.energy, E_all));
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rec_all_0 = gather(cat(4, tomogram_edensity{:}));
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% get a weighted average
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mrec = max(0,mean(rec_all_0 .* reshape(num_proj_all,1,1,1,[]) ,4)) / mean(num_proj_all);
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mask = mrec > graythresh(mrec);
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%%
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mask = imopen(mask, strel('disk',5));
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mask = imdilate(mask, strel('disk',5));
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mask = imfill(mask, 'holes');
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mask = Garray(mask);
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constraint_fnct = @(x)(max(0,x.*mask));
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for ii = 1:Nenergy
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tomogram_edensity{ii} = constraint_fnct(tomogram_edensity{ii});
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end
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gpu = gpuDevice;
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for iter = 1:Niter_SVD
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utils.verbose(1,' ====== Iteration %i ==== ', iter)
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rec_all = cat(4, tomogram_edensity{:});
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utils.verbose(2,'Available GPU memory = %3.1fGB', gpu.AvailableMemory/1e9)
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plotting.smart_figure(4)
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plotting.imagesc3D(cat(2, squeeze(rec_all(:,:,ceil(end/2),:)), squeeze(rec_all_0(:,:,ceil(end/2),:))));
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axis off image, colormap bone
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caxis(gather(math.sp_quantile(rec_all, [0.001, 0.9999], 10)));
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title('Left - SVD refined , Right - original FBP')
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rec_all = reshape(rec_all, [], Nenergy);
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% add more modes progressivelly for higher iteration number
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Nmodes_tmp = min(floor(iter^(1/3)), Nmodes);
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%%%%%%%%%%%%%%%%%%%% APPLY SVD CONSTRAINT %%%%%
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[U,S,V] = math.fsvd(rec_all, Nmodes_tmp);
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% enforce smoothness of the first V vector
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if iter > 1
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% plot convergence progress
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try
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err_total(iter,:) = gather(sqrt(sum((U*S*V'-rec_all).^2)));
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catch
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keyboard
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end
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plotting.smart_figure(3)
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loglog(mean(err_total'))
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axis tight
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grid on
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xlabel('Iteration')
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ylabel('Residuum between SVD model and reconstruction')
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drawnow
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end
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% relax = 0.1;
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% V(:,1) = V(:,1) *(1-relax) + relax * polyval(polyfit(1:Nenergy,V(:,1)',1), 1:Nenergy)';
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%
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% if Nmodes_tmp == 3
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% keyboard
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%
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% end
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if iter > 1
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% plot SVD evolution
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best_angle = fminsearch(@(x)get_rotation_score(x,U,S,V), zeros(3,1));
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R = rotation_matrix_3D(best_angle(1),best_angle(2),best_angle(3));
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R = R(1:Nmodes_tmp,1:Nmodes_tmp); % use only number of modes that is needed
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Vplot = (R*V')'; % apply rotation
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Uplot = U*S*inv(R); % apply inverse rotation
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% flip sign to for convinince
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sign_U = sign(mean(Uplot));
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Uplot = Uplot .* sign_U;
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Vplot = Vplot .* sign_U;
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rec_all = gather(rec_all);
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U_plot = Uplot ./ quantile(Uplot(1:32:end,:), 0.99);
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U_plot = reshape(U_plot, [size(tomogram_edensity{1}),Nmodes_tmp]);
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U_plot = reshape(permute(U_plot,[1,2,4,3]), [size(U_plot,1),size(U_plot,2)*size(U_plot,4),size(U_plot,3)]);
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plotting.smart_figure(5)
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subplot(2,1,1)
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plotting.imagesc3D(U_plot, 'init_frame', size(U_plot,3)/2)
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axis image off
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colormap bone
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caxis(gather(math.sp_quantile(U_plot, [0.001, 0.995], 10)));
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title('Topos SVD vectors')
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subplot(2,1,2)
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plot(E_all,Vplot, '-o')
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hold all
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offset = min(min(Vplot ));
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range = max(max(Vplot )) - offset;
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bar(E_all,num_proj_all / max(num_proj_all)*range*0.2+ offset, 'facecolor', 'none', 'Basevalue', offset)
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hold off
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title('Chronos SVD vectors')
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axis tight
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grid on
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xlabel('Energy [keV]')
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ylabel('S*V''')
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Energy = diag(S);
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Energy = Energy / sum(Energy);
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for kk = 1:Nmodes_tmp
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legend_txt{kk} = sprintf('E=%3.2g%%', Energy(kk)*100);
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end
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legend(legend_txt ,'location','best')
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clear U_plot
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end
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% ather from GPU to save memory
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% Uout = gather(Uout);
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% apply SART refinement
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for ii = 1:Nenergy
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utils.progressbar(ii,Nenergy)
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% choose projections to process
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rec_ind = find(par.energy == E_all(ii) & ismember(1:Nangles,reconstruct_ind)'); % use only some angles
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% downsample to the requested "max_projections"
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rec_ind = rec_ind(1:ceil(length(rec_ind)/max_projections):end);
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if isempty(rec_ind); continue; end
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[cache_SART,cfg_SART] = tomo.SART_prepare(cfg, vectors(rec_ind,:), SART_grouping, 'keep_on_GPU', true);
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rec = U*S*V(ii,:)';
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rec = reshape(rec,size(tomogram_edensity{1}));
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par.lambda = 1.234e-9 / E_all(ii);
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par.factor=par.lambda/(2*pi*par.pixel_size);
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par.factor_edensity = 1e-30*2*pi/(par.lambda^2*2.81794e-15);
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% get full reconstruction (for FBP is sum already final tomogram)
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% calculate complex refractive index
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rec = rec / (par.factor*par.factor_edensity);
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rec = Garray(rec);
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sino = Garray(sinogram(:,:,rec_ind));
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clear err
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for jj = 1:Niter_SART
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[rec,err(jj,:)] = tomo.SART(rec, sino, cfg_SART, ...
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vectors(rec_ind,:),cache_SART, 'relax', 0, 'constraint', constraint_fnct);
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end
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% apply some weak total variation to help agsints undersampling
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% artefacts
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rec = regularization.local_TV3D_chambolle(rec, 1e-6, 10);
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tomogram_edensity{ii} = (rec*par.factor*par.factor_edensity);
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% plotting.smart_figure(1)
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% subplot(1,3,1)
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% plotting.imagesc3D(tomogram_edensity{ii}); axis off image, colormap bone
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% caxis([0,1])
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% subplot(1,3,2)
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% plot(theta(rec_ind), 'o-')
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% title(['Nangles ', num2str(length(rec_ind)) ])
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% subplot(1,3,3)
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% loglog(mean(err'))
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% drawnow
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end
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clear rec sino cache_SART
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end
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rec_all = reshape(rec_all, [size(tomogram_edensity{1}), Nenergy]);
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% get recosntructions to RAM
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U = gather(U);
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S = gather(S);
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V = gather(V);
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rec_all = gather(rec_all);
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end
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function score = get_rotation_score(x,U,S,V)
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R = rotation_matrix_3D(x(1),x(2),x(3));
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Nmodes = size(S,1);
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V = (R(1:Nmodes,1:Nmodes)*V')';
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score = gather(norm(V(:,1) - mean(V(:,1))));
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end
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