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2026-09-17 21:49:08 +09:00 · 2026-08-07 15:56:42 +09:00
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+% SVD_regularize_3D_fields - use SVD to constraint the reconstructed DVF
+% and enforce smoothness in the DVF reconstruction 
+%
+%   shift_3D_total = SVD_regularize_3D_fields(shift_3D_total, Nsvd, SVD_smoothing)
+%
+% Inputs:
+%    **shift_3D_total - (cell of 3D arrays) recovered deformation field 
+%    **Nsvd - (int), maximal number of SVD modes to be recovered (should be less than number of subtomos)
+%    **SVD_smoothing - (scalar), smoothing constant between 0 to 0.25
+% returns:
+%    ++shift_3D_total - (cell of 3D arrays) regularized deformation field 
+
+
+%*-----------------------------------------------------------------------*
+%|                                                                       |
+%|  Except where otherwise noted, this work is licensed under a          |
+%|  Creative Commons Attribution-NonCommercial-ShareAlike 4.0            |
+%|  International (CC BY-NC-SA 4.0) license.                             |
+%|                                                                       |
+%|  Copyright (c) 2017 by Paul Scherrer Institute (http://www.psi.ch)    |
+%|                                                                       |
+%|       Author: CXS group, PSI                                          |
+%*-----------------------------------------------------------------------*
+% You may use this code with the following provisions:
+%
+% If the code is fully or partially redistributed, or rewritten in another
+%   computing language this notice should be included in the redistribution.
+%
+% If this code, or subfunctions or parts of it, is used for research in a 
+%   publication or if it is fully or partially rewritten for another 
+%   computing language the authors and institution should be acknowledged 
+%   in written form in the publication: “Data processing was carried out 
+%   using the “cSAXS matlab package” developed by the CXS group,
+%   Paul Scherrer Institut, Switzerland.” 
+%   Variations on the latter text can be incorporated upon discussion with 
+%   the CXS group if needed to more specifically reflect the use of the package 
+%   for the published work.
+%
+% A publication that focuses on describing features, or parameters, that
+%    are already existing in the code should be first discussed with the
+%    authors.
+%   
+% This code and subroutines are part of a continuous development, they 
+%    are provided “as they are” without guarantees or liability on part
+%    of PSI or the authors. It is the user responsibility to ensure its 
+%    proper use and the correctness of the results.
+
+
+function shift_3D_total = SVD_regularize_3D_fields(shift_3D_total, Nsvd, SVD_smoothing)
+
+        % SVD regularization 
+        Nblocks= length(shift_3D_total);
+        Nps = size(shift_3D_total{1}{1});
+        for kk = 1:3
+            for ll = 1:Nblocks
+                shift_3D_mat(:,:,:,kk,ll) = shift_3D_total{ll}{kk};
+            end
+        end
+        shift_3D_mat = reshape(shift_3D_mat,[],Nblocks);
+        [U,S,V] = fsvd(shift_3D_mat, min(Nsvd, Nblocks));
+        %% apply a bit of smoothness 
+        kernel = [SVD_smoothing, 1-2*SVD_smoothing, SVD_smoothing]'; 
+        V = conv2(V, kernel, 'same') ./ conv2(ones(Nblocks,min(Nsvd, Nblocks)), kernel, 'same') ; 
+        shift_3D_mat = U*S*V';
+        shift_3D_mat = reshape(shift_3D_mat, [Nps,3,Nblocks]);
+        for kk = 1:3
+            for ll = 1:Nblocks
+               shift_3D_total{ll}{kk} = shift_3D_mat(:,:,:,kk,ll);
+            end
+        end
+        
+end