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2026-09-17 20:39:08 +09:00 · 2026-08-07 15:56:42 +09:00
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+% get_deformation_fields - calculate the DVF from the observed deformation
+% field arrays bu deconvolution 
+%
+% [deform_tensors_linear, inv_deform_tensors_linear] = ...
+%                    get_deformation_fields(shift_tensors, regularize_lambda, Npix_vol)
+%
+% Inputs:
+%    **shift_tensors       observed deformation 
+%    **regularize_lambda   regularization constant for the deconvolution 
+%    **Npix_vol            size of the reconstructed volume  
+% Outputs: 
+%    ++deform_tensors_linear        calculate forward DVF 
+%    ++inv_deform_tensors_linear    calculate inverse DVF 
+
+%*-----------------------------------------------------------------------*
+%|                                                                       |
+%|  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) 2018 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 [deform_tensors_linear, inv_deform_tensors_linear] = ...
+                    get_deformation_fields(shift_tensors, regularize_lambda, Npix_vol)
+    % simple deconvolution of the recovered shift arrays to the object
+    % defomration arrays for linear deformation model 
+    
+    
+    Nblocks = length(shift_tensors); 
+    
+    if Nblocks == 1
+       error('Number of blocks (subtomos) has to be > 1') 
+    end
+    
+    if Nblocks > 1
+        conv_mat = spdiags(ones(Nblocks,1),0,Nblocks, Nblocks+1) + spdiags(ones(Nblocks,1),1,Nblocks, Nblocks+1); 
+        conv_mat = conv_mat ./ sum(conv_mat,2);
+        regul_mat = spdiags(2*ones(Nblocks,1), 0, Nblocks, Nblocks+1) - spdiags(ones(Nblocks,1), 1, Nblocks, Nblocks+1)-spdiags(ones(Nblocks,1), -1, Nblocks, Nblocks+1);
+        regul_mat(1,1:2) = 0;
+
+        deform_mat = [];
+        for block = 1:Nblocks
+            for ax = 1:3
+                deform_mat(:,:,:,ax,block) = gather(shift_tensors{block}{ax}); 
+            end
+        end
+        size_deform_mat = size(deform_mat); 
+        deform_mat = reshape(deform_mat, [], Nblocks); 
+
+        %% perform Tikhonov based deconvolution 
+
+%         N = 50;
+%         lams = logspace(-5,1,N);
+%         for i = 1:N
+            deconv_def_mat = ((conv_mat'*conv_mat + regularize_lambda*regul_mat'*regul_mat)\(conv_mat'*deform_mat'))';
+            % enforce zero for the first deformation 
+            deconv_def_mat = deconv_def_mat - deconv_def_mat(:,1); 
+
+%             err(i) = math.mean2((conv_mat*deconv_def_mat' - deform_mat').^2);
+%         end
+        
+
+        deconv_def_mat = reshape(deconv_def_mat,[size_deform_mat(1:4), Nblocks+1] ); 
+        for block = 1:Nblocks+1
+            for ax = 1:3
+                deform_tensors{block}{ax} = single(deconv_def_mat(:,:,:,ax,block)); 
+            end
+        end
+    else
+       deform_tensors =  shift_tensors; 
+    end
+    
+    [deform_tensors,inv_deform_tensors] =  nonrigid.invert_DVF(deform_tensors, Npix_vol)   ;
+    
+    % join blocks to keep initial and final deform for each block together
+    % -> linear deformation evolution is assumed in between 
+    if Nblocks > 1
+        for block = 1:Nblocks
+            deform_tensors_linear{block} = [deform_tensors{block}; deform_tensors{block+1}]; 
+            inv_deform_tensors_linear{block} = [inv_deform_tensors{block}; inv_deform_tensors{block+1}]; 
+        end
+    else  % just assume one single deformation 
+        deform_tensors_linear = deform_tensors; 
+        inv_deform_tensors_linear = inv_deform_tensors; 
+    end
+    
+
+end