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% FBP_PROPAGATION filtered back propagation for diffraction tomography
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%
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% [rec] = FBP_propagation(sino, theta, variable, par, optimal_propagation)
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%
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% Inputs:
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% **sino - sinogram (Nlayers x width x Nangles)
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% **angles - projection angles
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% **variable - 'phase' or 'amplitude'
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% **par - parameter structure
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% **optimal_propagation - position of center of focus
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% *returns*
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% ++rec - reconstructed volume
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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 [rec_volume] = FBP_propagation(sino, theta, variable, par, optimal_propagation, thickness)
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% Filtered backpropagation
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% assert(~isreal(sino), 'Input sinogram has to be complex-valued')
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[Nlayers, width_sinogram, Nangles] = size(sino);
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assert(length(theta)==Nangles, 'Size of sinogram does not correspond to size of Nangles');
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% create a matrix of propagation through entire sample
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if nargin < 6
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propag = -single(par.pixel_size*(-ceil(width_sinogram/2):floor(width_sinogram/2-1)));
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else
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propag = -single(linspace(-thickness/2,thickness/2, width_sinogram));
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end
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[~,H0] = utils.prop_free_nf(ones(Nlayers,width_sinogram,'single'), par.lambda, propag, par.pixel_size);
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%% allocate shared memory
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use_sharemem = false;
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if use_sharemem
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%% allocate reconstruction volume
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rec_volume = zeros(width_sinogram, width_sinogram, Nlayers, 'single');
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share_mem = shm(true);
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share_mem.allocate(rec_volume);
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share_mem.detach();
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else
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%% allocate reconstruction volume
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rec_volume = gpuArray.zeros(width_sinogram, width_sinogram, Nlayers, 'single');
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H0 = gpuArray(H0);
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end
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% create a support mask that limits extend of the reconstruction
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[~,circle] = utils.apply_3D_apodization(rec_volume,50,0,0.1);
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circle = single(circle);
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%% solve the FBP task
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for ii = 1:Nangles
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utils.progressbar(ii, Nangles, 100);
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rec_volume = calculate_filt_back_propagation(rec_volume, sino(:,:,ii), theta(ii),circle,H0, par, variable, optimal_propagation(min(ii,end)));
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end
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if use_sharemem
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[share_mem, rec_shm] = share_mem.attach();
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rec_volume(:) = rec_shm;
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share_mem.detach();
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end
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rec_volume = gather(rec_volume);
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end
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function rec_volume = calculate_filt_back_propagation(rec_volume, sino_tmp, theta, circle, H0, par, variable, optimal_propagation, thickness)
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[Nlayers, width_sinogram] = size(sino_tmp);
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sino_tmp = propagate_sinogram(H0, sino_tmp, par,variable, optimal_propagation);
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sino_tmp = permute(sino_tmp, [3,2,1]);
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cfg.iProjV = size(sino_tmp,1);
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cfg.iProjU = width_sinogram;
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cfg.iProjAngles = Nlayers;
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% apply filtering, dont do any backprojetion
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[~,sino_filt] = tomo.FBP(sino_tmp, cfg, zeros(Nlayers,12), 1,'verbose',0, 'determine_weights', false, 'GPU', par.GPU_list, 'filter', 'ram-lak', 'only_filter_sinogram', true);
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if isscalar(H0)
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sino_filt = repmat(sino_filt,width_sinogram,1,1);
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end
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sino_filt = sino_filt .* circle;
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%% rotate propagated projections
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% sino_filt = utils.imrotate_ax_fft(sino_filt, theta(ii), 3); % subpixel precision inteprolation using FFT
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sino_filt = utils.imrotate_ax(sino_filt, theta, 3); % common linear interpolation
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%% add filtered update to the total reconstruction
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if isa(rec_volume, 'shm')
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[share_mem, rec_volume] = rec_volume.attach();
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tomo.set_to_array(rec_volume, gather(sino_filt), 0, true); % write directly to the shared memory
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share_mem.detach();
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else
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rec_volume = rec_volume + sino_filt;
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end
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end
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function sinogram = propagate_sinogram(H0, sinogram, par,variable, optimal_propagation)
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[Nlayers, width_sinogram, ~] = size(sinogram);
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sinogram = gpuArray(sinogram);
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%% FT interpolation + NF propagation
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if any(optimal_propagation > 0)
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H = gpuArray.ones(Nlayers,width_sinogram,'single');
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[~,H] = utils.prop_free_nf(H, par.lambda, optimal_propagation, par.pixel_size);
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else
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H = 1;
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end
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if ~isscalar(H0) || ~isscalar(H)
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% propagate along the beam
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sinogram = ifft2(fft2(sinogram).*H0.* H);
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end
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switch variable
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case 'amplitude'
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%% get amplitude
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sinogram = -log(abs(sinogram));
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case 'phase'
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%% get phase
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sinogram = -math.unwrap2D_fft(sinogram,2, [10,10], 0);
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otherwise
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error('Wrong option')
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end
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end
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