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% [U,S,V,rec_all] = SART_SVD(sinogram, theta, Npix, blocks, par)
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% perform temporal SVD analysis and SART based reconstruction to
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% estimate changes of the sample during reconstruction
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% Inputs:
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% **sinogram unwrapped sinogram
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% **theta tomography angles
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% **Npix size of the reconstructed volume
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% **blocks cell list containing indices for each subtomogram
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% Outputs:
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% ++U,S,V singular vectors
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% ++rec_all SVD filterd reconstruction for each subtomogram
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% Example of use:
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% subtomo_ind = [1, find(abs(diff(theta))> 170), length(theta)];
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% for ii = 1:length(subtomo_ind)-1
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% ind{ii} = subtomo_ind(ii):subtomo_ind(ii+1);
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% end
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% [U,S,V] = nonrigid.SART_SVD(sinogram, theta, Npix, ind);
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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) 2018 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] = SART_SVD(sinogram, theta, Npix, blocks, varargin)
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p = inputParser;
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p.addOptional('split', 1)
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p.addParameter('valid_angles', [])
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p.addParameter('SART_grouping', 25 ) % size of blocks in SART, ART=1, SIRT=Nangles
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p.addParameter('GPU', []) % list of GPUs to be used in reconstruction
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p.addParameter('verbose', 1) % verbose = 0 : quiet, verbose : standard info , verbose = 2: debug
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p.addParameter('N_SVD_modes', 2) % number of recovered SVD modes, 2 is usually enough
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p.addParameter('Niter_SVD', 3) % number of iter of the SVD SART
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p.addParameter('Niter_SART', 5) % number of internal iterations in each SART loops
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p.addParameter('output_folder', '') % path where the results should be stored
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p.addParameter('mask', []) % mask applied on the reconstruction
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p.parse(varargin{:})
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res = p.Results;
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utils.verbose(1,'Using FBP for initial guess')
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Nblocks = length(blocks);
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tomogram = cell(Nblocks,1);
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for ii = 1:Nblocks
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utils.progressbar(ii,Nblocks)
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% choose projections to process
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rec_ind = setdiff(blocks{ii}, res.valid_angles);
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%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%
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[Nlayers,width_sinogram,~] = size(sinogram);
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[cfg, vectors] = astra.ASTRA_initialize([Npix,Npix, Nlayers],[Nlayers,width_sinogram],theta);
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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(res.GPU), 1);
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% new FBP code
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subtomogram = tomo.FBP_zsplit(sinogram, cfg, vectors, split,'valid_angles',rec_ind,...
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'determine_weights', true, ...
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'GPU', res.GPU ,'filter','ram-lak', 'filter_value',1, 'verbose',-1);
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num_proj_all(ii) = length(rec_ind);
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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{ii} = gather(subtomogram);
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end
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if isempty(res.mask)
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constraint_fnct= @(x)x;
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else
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constraint_fnct = @(x)(abs(x).*res.mask);
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end
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for ii = 1:Nblocks
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tomogram{ii} = constraint_fnct(tomogram{ii});
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end
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gpu = gpuDevice;
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for iter = 1:res.Niter_SVD
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utils.verbose(1,' ====== Iteration %i/%i ==== ', iter,res.Niter_SVD)
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rec_all = cat(4, tomogram{:});
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utils.verbose(2,'Available GPU memory = %3.1fGB', gpu.AvailableMemory/1e9)
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rec_all = reshape(rec_all, [], Nblocks);
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%% %%%%%%%%%%%%%%%%%% APPLY SVD CONSTRAINT %%%%%
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utils.verbose(0,'Calculating SVD ... ')
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Nmodes = min(iter, res.N_SVD_modes);
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[U,S,V] = math.fsvd(rec_all, Nmodes);
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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if Nmodes == res.N_SVD_modes
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err_total(iter,:) = gather(sqrt(sum((U*S*V'-rec_all).^2)));
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%% plot convergence progress
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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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title('SVD SART - Convergence evolution')
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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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utils.verbose(0,'Calculating SART ... ')
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% apply SART refinement
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for ii = 1:Nblocks
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utils.progressbar(ii,Nblocks)
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% choose projections to process
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rec_ind = setdiff(blocks{ii}, res.valid_angles);
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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,:), res.SART_grouping, 'keep_on_GPU', true, 'verbose', 0);
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rec = U*S*V(ii,:)';
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rec = reshape(rec,size(tomogram{1}));
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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 = utils.Garray(rec);
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sino = utils.Garray(sinogram(:,:,rec_ind));
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clear err
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for jj = 1:res.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, 'verbose', 0);
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end
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% apply some weak total variation to help againts undersampling
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% artefacts
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%rec = regularization.local_TV3D_chambolle(rec, 1e-6, 10);
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tomogram{ii} = gather(rec);
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end
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clear rec sino cache_SART
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end
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%% plot SVD evolution
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rec_all = reshape(U*S*V', Npix, Npix,size(sinogram,1), Nblocks);
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rec_all = reshape(rec_all, [size(tomogram{1}), Nblocks]);
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V_sign = sign(mean(V));
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U(:,1) = U(:,1).*V_sign(1);
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V(:,1) = V(:,1).*V_sign(1);
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screensize = get( 0, 'Screensize' );
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plotting.smart_figure(11)
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subplot(1,2,1)
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plotting.imagesc3D(squeeze(rec_all(:,:,ceil(end/2),:)))
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axis image off
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colormap bone
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caxis(gather(math.sp_quantile(rec_all, [0.001, 0.995], 10)));
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plotting.suptitle('Tomogram evolution in each subtomogram (central slice)')
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subplot(1,2,2)
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plot(V, '-o')
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title('Principal components evolution')
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axis tight
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grid on
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xlabel('Block')
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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:res.N_SVD_modes
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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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set(gcf,'Outerposition',[1 screensize(4)-500 800 500]);
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if ~isempty(res.output_folder) && ~debug()
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try
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savefig(fullfile(res.output_folder, 'SVD_filtered_evolution.fig'))
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catch err
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warning('Saving of SVD_filtered_evolution failed with error: %s', err.message)
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end
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end
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U = reshape(U, [size(tomogram{1}), res.N_SVD_modes]);
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U_plot = U(:,:,2:end-1,:); % it seems that first and last layer are not well estimated
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U_plot = U_plot - median(quantile(min(U_plot,[],1),0.01,2),3);
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U_plot = U_plot ./ median(quantile(max(U_plot,[],1),0.99,2),3);
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%
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U_plot = cat(2, U_plot(:,:,:,1), U_plot(:,:,:,2));
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plotting.smart_figure(10)
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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('Principal components (left is 1th PC , right is 2nd PC)')
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subplot(2,1,2)
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plotting.imagesc3D(U_plot, 'init_frame', size(U_plot,1)/2, 'slider_axis',1)
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axis image off
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colormap bone
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title('Principal components (left is 1th PC , right is 2nd PC)')
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caxis(gather(math.sp_quantile(U_plot, [0.001, 0.995], 10)));
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%%%suptitle('Principal vectors showing tomogram evolution (slide to see layers of the sample)')
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set(gcf,'Outerposition',[1 screensize(4)-1250 1200 700]);
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if ~isempty(res.output_folder) && ~debug()
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print('-f10','-dpng','-r300',[res.output_folder, '/SVD_modes_scaled.png']);
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end
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%% get reconstructions 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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U = reshape(U, [Npix, Npix,size(sinogram,1),res.N_SVD_modes]);
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end
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