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103 lines
3.6 KiB
Matlab
103 lines
3.6 KiB
Matlab
% function f = local_TV3D_chambolle(f, lambda, niter)
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% apply local total variation usiniter matlab functions, it uses chambolle
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% solver -> faster but more memory demanding
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% Inputs: f - 3D array to be regularized
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% lambda - constant to be tuned
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% niter - number of iterations
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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 followiniter 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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% computiniter laniteruage 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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% computiniter laniteruage the authors and institution should be acknowledged
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% in written form in the publication: “Data processiniter was carried out
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% usiniter 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 describiniter features, or parameters, that
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% are already existiniter 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 x = local_TV3D_chambolle(x,lambda, niter)
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[M,N,O] = size(x);
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if lambda == 0
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return
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end
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x0 = x;
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xi = zeros(M,N,O,3, class(x));
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tau=2/8;
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%%% INNER LOOP
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for iinner = 1:niter
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% chambolle step
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gdv = grad( div(xi) - x/lambda );
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%% isotropic
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% d = sqrt(sum(gdv.^2,3));
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%% anisotropic
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d = sum( abs(gdv), 4);
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xi = bsxfun(@times, xi + tau*gdv, 1 ./ ( 1+tau*d ));
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% reconstruct
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x = x - lambda*div( xi );
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end
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% prevent pushing values to zero by the TV regularization
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x = sum(x0(:).* x(:)) / sum(x(:).^2) * x;
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end
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function fd = div(P)
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% div - divergence (backward difference)
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%
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% fd = div(P);
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Px = P(:,:,:,1);
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Py = P(:,:,:,2);
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Pz = P(:,:,:,3);
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fx = Px-Px([1 1:end-1],:,:);
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fy = Py-Py(:,[1 1:end-1],:);
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fz = Pz-Pz(:,:,[1 1:end-1]);
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fd = fx+fy+fz;
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end
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function f = grad(M)
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% grad - gradient, forward differences
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% g = grad(M);
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fx = M([2:end end],:,:)-M;
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fy = M(:,[2:end end],:)-M;
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fz = M(:,:,[2:end end])-M;
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f = cat(4,fx,fy,fz);
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end |