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tomo/+regularization/local_TV3D_grad.m

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+% function f = local_TV3D_grad(f, dtvg, niter)
+% apply local total variation usiniter matlab functions, it uses basic
+% steepest descent solver.
+%  Inputs: f - 3D array to be regularized 
+%          dtvg - gradient descent step (constant to be tuned)
+%          niter - number of iterations 
+
+
+%*-----------------------------------------------------------------------*
+%|                                                                       |
+%|  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 followiniter provisions:
+%
+% If the code is fully or partially redistributed, or rewritten in another
+%   computiniter laniteruage 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 
+%   computiniter laniteruage the authors and institution should be acknowledged 
+%   in written form in the publication: “Data processiniter was carried out 
+%   usiniter 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 describiniter features, or parameters, that
+%    are already existiniter 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 f = local_TV3D_grad(f, dtvg, niter)
+    for ii=1:niter
+        % Steepest descend of TV norm
+        %% CUDA version will make it more memory effecient => almost inplace !! 
+        df=gradientTVnormForward(f);
+        df=df./sqrt(mean(df(:).^2)); % it will be close to 1 anyway
+        f=f-dtvg.*df;
+    end 
+end
+    
+
+%% Forward differences
+function tvg=gradientTVnormForward(f)
+    % gradient 
+    
+    Gx=diff(f,1,1);
+    Gy=diff(f,1,2);
+    Gz=diff(f,1,3);
+    
+    Gx=cat(1,Gx,zeros(size(Gx(end,:,:)), class(f)));
+    Gy=cat(2,Gy,zeros(size(Gy(:,end,:)), class(f)));
+    Gz=cat(3,Gz,zeros(size(Gz(:,:,end)), class(f)));
+    
+    nrm=sqrt(Gx.^2+Gy.^2+Gz.^2)+1e-7;
+
+    % divergence 
+    tvg=Gx([1,1:end-1],:,:)-Gx + Gy(:,[1,1:end-1],:)-Gy+Gz(:,:,[1,1:end-1])-Gz;
+    tvg=tvg ./ nrm;
+end
+