% Main code to compute error metric and gradient % Jan 09 2013 % Academic License Agreement % % Source Code % % Introduction % • This license agreement sets forth the terms and conditions under which the PAUL SCHERRER INSTITUT (PSI), CH-5232 Villigen-PSI, Switzerland (hereafter "LICENSOR") % will grant you (hereafter "LICENSEE") a royalty-free, non-exclusive license for academic, non-commercial purposes only (hereafter "LICENSE") to use the cSAXS % ptychography MATLAB package computer software program and associated documentation furnished hereunder (hereafter "PROGRAM"). % % Terms and Conditions of the LICENSE % 1. LICENSOR grants to LICENSEE a royalty-free, non-exclusive license to use the PROGRAM for academic, non-commercial purposes, upon the terms and conditions % hereinafter set out and until termination of this license as set forth below. % 2. LICENSEE acknowledges that the PROGRAM is a research tool still in the development stage. The PROGRAM is provided without any related services, improvements % or warranties from LICENSOR and that the LICENSE is entered into in order to enable others to utilize the PROGRAM in their academic activities. It is the % LICENSEE’s responsibility to ensure its proper use and the correctness of the results.” % 3. THE PROGRAM IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR % A PARTICULAR PURPOSE AND NONINFRINGEMENT OF ANY PATENTS, COPYRIGHTS, TRADEMARKS OR OTHER RIGHTS. IN NO EVENT SHALL THE LICENSOR, THE AUTHORS OR THE COPYRIGHT % HOLDERS BE LIABLE FOR ANY CLAIM, DIRECT, INDIRECT OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY ARISING FROM, OUT OF OR IN CONNECTION WITH THE PROGRAM OR THE USE % OF THE PROGRAM OR OTHER DEALINGS IN THE PROGRAM. % 4. 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LICENSEE agrees that it shall make the following acknowledgement in any publication resulting from the use of the PROGRAM or any translation of the code into % another computing language: % "Data processing was carried out using the cSAXS ptychography MATLAB package developed by the Science IT and the coherent X-ray scattering (CXS) groups, Paul % Scherrer Institut, Switzerland." % % Additionally, any publication using the package, or any translation of the code into another computing language should cite for difference map: % P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, High-resolution scanning X-ray diffraction microscopy, Science 321, 379–382 (2008). % (doi: 10.1126/science.1158573), % for maximum likelihood: % P. Thibault and M. Guizar-Sicairos, Maximum-likelihood refinement for coherent diffractive imaging, New J. Phys. 14, 063004 (2012). % (doi: 10.1088/1367-2630/14/6/063004), % for mixed coherent modes: % P. Thibault and A. Menzel, Reconstructing state mixtures from diffraction measurements, Nature 494, 68–71 (2013). (doi: 10.1038/nature11806), % and/or for multislice: % E. H. R. Tsai, I. Usov, A. Diaz, A. Menzel, and M. Guizar-Sicairos, X-ray ptychography with extended depth of field, Opt. Express 24, 29089–29108 (2016). % (doi: 10.1364/OE.24.029089). % 6. Except for the above-mentioned acknowledgment, LICENSEE shall not use the PROGRAM title or the names or logos of LICENSOR, nor any adaptation thereof, nor the % names of any of its employees or laboratories, in any advertising, promotional or sales material without prior written consent obtained from LICENSOR in each case. % 7. Ownership of all rights, including copyright in the PROGRAM and in any material associated therewith, shall at all times remain with LICENSOR, and LICENSEE % agrees to preserve same. LICENSEE agrees not to use any portion of the PROGRAM or of any IMPROVEMENTS in any machine-readable form outside the PROGRAM, nor to % make any copies except for its internal use, without prior written consent of LICENSOR. LICENSEE agrees to place the following copyright notice on any such copies: % © All rights reserved. PAUL SCHERRER INSTITUT, Switzerland, Laboratory for Macromolecules and Bioimaging, 2017. % 8. The LICENSE shall not be construed to confer any rights upon LICENSEE by implication or otherwise except as specifically set forth herein. % 9. DISCLAIMER: LICENSEE shall be aware that Phase Focus Limited of Sheffield, UK has an international portfolio of patents and pending applications which relate % to ptychography and that the PROGRAM may be capable of being used in circumstances which may fall within the claims of one or more of the Phase Focus patents, % in particular of patent with international application number PCT/GB2005/001464. The LICENSOR explicitly declares not to indemnify the users of the software % in case Phase Focus or any other third party will open a legal action against the LICENSEE due to the use of the program. % 10. This Agreement shall be governed by the material laws of Switzerland and any dispute arising out of this Agreement or use of the PROGRAM shall be brought before % the courts of Zürich, Switzerland. function [func, grad, p] = gradient_ptycho(xopt,p,fmag2, initialerror,fnorm,creg,smooth_gradient) import utils.verbose %%% Initialize variables %%% func = 0; % Should be zero except for poisson (factorial factor) for ii = 1:p.numobjs grado{ii} = zeros([p.object_size(ii,:) p.object_modes], 'like', xopt)+1i*eps; end gradp = zeros(p.asize(1),p.asize(2),p.numprobs,p.probe_modes, 'like', xopt)+1i*eps; % gradx = zeros(n,1); % grady = zeros(n,1); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Arrange optimization variables %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if p.opt_flags(1) == 1, for obnum = 1:p.numobjs % ob{obnum} = reshape(xopt(1:p.object_size(obnum,1)*p.object_size(obnum,2)),... % p.object_size(obnum,1),p.object_size(obnum,2)) + ... % 1i*reshape(xopt(p.object_size(obnum,1)*p.object_size(obnum,2)+1:2*p.object_size(obnum,1)*p.object_size(obnum,2)),... % p.object_size(obnum,1),p.object_size(obnum,2)); ob{obnum} = reshape(xopt(1:numel(grado{obnum})),... size(grado{obnum})) + ... 1i*reshape(xopt(numel(grado{obnum})+1:2*numel(grado{obnum})),... size(grado{obnum})); xopt = xopt(2*numel(grado{obnum})+1:end); end end if p.opt_flags(2) == 1, probes = reshape(xopt(1:numel(gradp)),size(gradp)) + ... 1i*reshape(xopt(numel(gradp)+1:2*numel(gradp)),size(gradp)); xopt = xopt(2*numel(gradp)+1:end); end % if flags(3) == 1, % x = tmp(1:params.n); % y = tmp(params.n+1:2*params.n); % end %%%%%%%%%%%%%%%%%%%%% %%% Support error %%% %%%%%%%%%%%%%%%%%%%%% % Option to add later for a smooth support constraint error %%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Compute error metric %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Still to implement here: % + L1 and L2 metrics % + Insensitive to multiplicative scale if nargout > 1 verbose(3,'Computing gradient') end for ii = 1:p.numscans prnum = p.share_probe_ID(ii); obnum = p.share_object_ID(ii); probe = probes(:,:,prnum,:); Iq_all = 0; for obmode = 1:p.object_modes obj_proj{obmode} = core.get_projections(p, ob{obnum}(:,:,obmode), ii); psiq_all{obmode} = fft2(bsxfun(@times,obj_proj{obmode},probe/fnorm)); % view in Fourier domain Iq_all = Iq_all + sum(abs(psiq_all{obmode}).^2,4); end % Use implicit matlab paralelization to avoid computational overhead , % currenly implemented only for L1 norm if strcmpi(p.opt_errmetric,'l1') fmag = p.fmag(:,:,p.scanidxs{ii}); fmask = p.fmask(:,:,p.scanidxs{ii}); Fq = sqrt(Iq_all); %%% Invariant to intensity fluctuations if p.inv_intensity alpha = sum(sum(fmask.*fmag.*Fq))./sum(sum(fmag.*Fq.^2)); else alpha = 1; end func = sum(sum(sum(fmask.*( alpha.*Fq - fmag ).^2))); if nargout > 1 % Compute gradients for obmode = 1:p.object_modes chir = alpha.*ifft2(fmask.*( alpha - fmag./(Fq+eps) ).*psiq_all{obmode})*fnorm; % May not be needed for position optimization if p.opt_flags(1) == 1, grado{obnum}(:,:,obmode) = core.set_projections(p, grado{obnum}(:,:,obmode), sum(2*conj(probe).*chir,4), ii); end if p.opt_flags(2) == 1 gradp(:,:,prnum,:) = gradp(:,:,prnum,:) ... + sum(2*conj(obj_proj{obmode}).*chir,3); end end end else for jj = p.scanidxs{ii} % Loop through diffraction patterns Indy = round(p.positions(jj,1)) + (1:p.asize(1)); Indx = round(p.positions(jj,2)) + (1:p.asize(2)); Iq = Iq_all(:,:,jj-p.scanidxs{ii}(1)+1); switch lower(p.opt_errmetric) case 'poisson' %%% Invariant to intensity fluctuations if p.inv_intensity % The numerator could be computed once outside alpha = sum(sum(p.fmask(:,:,jj).*fmag2(:,:,jj)))/sum(sum(p.fmask(:,:,jj).*Iq)); else alpha = 1; end func = func - sum(sum(p.fmask(:,:,jj).*( fmag2(:,:,jj).*log(alpha*Iq) - alpha*Iq ))); if nargout > 1 % Compute gradients for obmode = 1:p.object_modes psiq = psiq_all{obmode}(:,:,jj); % view in Fourier domain chir = ifft2(p.fmask(:,:,jj).*( alpha - fmag2(:,:,jj)./Iq ).*psiq)*fnorm; % May not be needed for position optimization for prmode = 1:p.probe_modes if p.opt_flags(1) == 1 grado{obnum}(Indy,Indx,obmode) = grado{obnum}(Indy,Indx,obmode) ... + sum(2*conj(probe).*chir, 4); end if p.opt_flags(2) == 1 gradp(:,:,prnum,:) = gradp(:,:,prnum,:) ... + 2*conj(ob{obnum}(Indy,Indx,obmode)).*chir; end end end end case 'l2' %%% Invariant to intensity fluctuations if p.inv_intensity alpha = sum(sum(p.fmask(:,:,jj).*fmag2(:,:,jj).*Iq))/sum(sum(p.fmask(:,:,jj).*Iq.^2)); else alpha = 1; end tmp = alpha*Iq - fmag2(:,:,jj); func = func + sum(sum(p.fmask(:,:,jj).*( tmp ).^2)); if nargout > 1 % Compute gradients for obmode = 1:p.object_modes psiq = psiq_all{obmode}(:,:,jj); % view in Fourier domain chir = alpha*ifft2(2*p.fmask(:,:,jj).*( tmp ).*psiq)*fnorm; % May not be needed for position optimization if p.opt_flags(1) == 1 grado{obnum}(Indy,Indx,obmode) = grado{obnum}(Indy,Indx,obmode) ... + sum(2*conj(probe).*chir,4); end if p.opt_flags(2) == 1 gradp(:,:,prnum,:) = gradp(:,:,prnum,:) ... + 2*conj(ob{obnum}(Indy,Indx,obmode)).*chir; end end end case 'l1' % %%% Invariant to intensity fluctuations % if p.inv_intensity % alpha = sum(sum(p.fmask(:,:,jj).*p.fmag(:,:,jj).*Fq))/sum(sum(p.fmask(:,:,jj).*Fq.^2)); % else % alpha = 1; % end % func = func + sum(sum(p.fmask(:,:,jj).*( alpha*Fq - p.fmag(:,:,jj) ).^2)); % if nargout > 1 % Compute gradients % for obmode = 1:p.object_modes % psiq = fft2(ob{obnum}(Indy,Indx,obmode).*probes(:,:,prnum,:))/fnorm; % view in Fourier domain % chir = alpha*ifft2(p.fmask(:,:,jj).*( alpha - p.fmag(:,:,jj)./(Fq+eps) ).*psiq)*fnorm; % May not be needed for position optimization % if p.opt_flags(1) == 1, % grado{obnum}(Indy,Indx,obmode) = grado{obnum}(Indy,Indx,obmode) ... % + sum(2*conj(probes(:,:,prnum,:)).*chir,4); % end % if p.opt_flags(2) == 1 % gradp(:,:,prnum,:) = gradp(:,:,prnum,:) ... % + 2*conj(ob{obnum}(Indy,Indx,obmode)).*chir; % end % end % end otherwise error(['Error metric ' p.opt_errmetric 'is not defined']) end end end end func = func + initialerror; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Sieves preconditioning %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if (any(smooth_gradient(:)) ~= 0)&&p.opt_flags(1) for obnum = 1:p.numobjs for obmode = 1:p.object_modes grado{obnum}(:,:,obmode) = conv2(grado{obnum}(:,:,obmode),smooth_gradient,'same'); end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Object regularization %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Normalized regularization to avoid the reduction of object amplitudes % with the setting of intensity invariant if (creg > 0)&&p.opt_flags(1) for obnum = 1:p.numobjs for obmode = 1:p.object_modes % Not normalized regularization % func = func ... % + sum(sum( abs( ob{obnum}(2:end,1:end-1) - ob{obnum}(1:end-1,1:end-1) ).^2 ... % + abs( ob{obnum}(1:end-1,2:end) - ob{obnum}(1:end-1,1:end-1) ).^2 )); R = sum(sum( abs( ob{obnum}(2:end,1:end-1,obmode) - ob{obnum}(1:end-1,1:end-1,obmode) ).^2 ... + abs( ob{obnum}(1:end-1,2:end,obmode) - ob{obnum}(1:end-1,1:end-1,obmode) ).^2 )); norm_r = sum(sum(abs(ob{obnum}(:,:,obmode)).^2)); func = func + creg*R/norm_r; if nargout > 1 % % Not normalized regularization % grado{obnum}(2:end-1,2:end-1) = grado{obnum}(2:end-1,2:end-1) + 8*ob{obnum}(2:end-1,2:end-1) ... % - 2*ob{obnum}(1:end-2,2:end-1) - 2*ob{obnum}(3:end,2:end-1) ... % - 2*ob{obnum}(2:end-1,1:end-2) - 2*ob{obnum}(2:end-1,3:end); grado{obnum}(2:end-1,2:end-1,obmode) = grado{obnum}(2:end-1,2:end-1,obmode) + creg*( (8+2*R/norm_r)*ob{obnum}(2:end-1,2:end-1,obmode) ... - 2*ob{obnum}(1:end-2,2:end-1,obmode) - 2*ob{obnum}(3:end,2:end-1,obmode) ... - 2*ob{obnum}(2:end-1,1:end-2,obmode) - 2*ob{obnum}(2:end-1,3:end,obmode)); end end end end % normalized error, err_chi close to 1 is good result for poisson noise err_chi = 2*sqrt(func/prod(p.asize)/p.numpos/p.renorm^2); func = double(func); if nargout > 1 core.errorplot(err_chi); iteration = length(core.errorplot([])); verbose(2, 'Iteration # %d of %d', iteration, p.opt_iter); verbose(3,['Starting linesearch, Error = ' num2str(err_chi)]), else verbose(3,['Error = ' num2str(err_chi)]), end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Probe support constratint %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if p.use_probe_support&&p.opt_flags(2) gradp = bsxfun(@times, gradp, p.probe_mask); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Scaling preconditioning %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% avobint = 0; if p.scale_gradient&&p.opt_flags(2) for ii = 1:p.numscans if p.share_probe avobint = avobint + sum( abs(grado{ii}(:)).^2 ); if ii == p.numscans avobint = avobint/p.numscans; gradp = sqrt( avobint/sum( abs(gradp(:)).^2 ) )*gradp; end else gradp(:,:,ii,:) = sqrt( sum( abs(grado{ii}(:)).^2 )/sum(sum(sum( abs(gradp(:,:,ii,:)).^2 ))) )*gradp(:,:,ii,:); end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Arranging gradients vector %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if nargout > 1 grad = []; % Optimization vector if p.opt_flags(1) == 1, for obnum = 1:p.numobjs grad = [grad; real(grado{obnum}(:)); imag(grado{obnum}(:))]; end end if p.opt_flags(2) == 1, grad = [grad; real(gradp(:)); imag(gradp(:))]; end % if flags(3) == 1, % xopt = [xopt;x;y]; % else % fixed.x = x; % fixed.y = y; % end if isempty(grad), error('At least one element of flags must be 1'), end %%%%%%%%%%%%%%% %%% Display %%% %%%%%%%%%%%%%%% p.error_metric.value = core.errorplot([]); p.error_metric.iteration = (1:size(core.errorplot([]),1)); p.error_metric.err_metric = '-LogLik'; p.error_metric.method = 'ML'; p.object = ob; p.probes = probes; if p.use_display if (round(mod(iteration,p.plot.interval))==0)||(iteration==1) p.plot.extratitlestring = sprintf(' (%dx%d) - iter %d', p.asize(2), p.asize(1), iteration); p.flat_object_used = 0; core.analysis.plot_results(p, 'use_display', p.use_display); end end end return end