%BACK_PROJ backpropagate the updated projections (multilayer slices) into
%the full 3D volume, call thi function separatelly for real and imaginary
%part of the projections 
%
% volData_upd = back_proj(projData_upd,theta,Npx_vol)
% 
%  Inputs: 
%   **projData_upd - stacked 2D array, linearized difference of the complex-valued projections, ie log( P_new .* conj(P_orig) ./ |P_orig|^2)
%   **theta        - scalar, angle of the provided projection  
%   **Npx_vol      - dimensions of the full volume 
%  *returns*
%   ++volData_upd  - 3D array, linearized update of the tomographic volume 


% 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 PtychoShelves 
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% 5.	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 
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%       "Data processing was carried out using the PtychoShelves 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 
% K. Wakonig, H.-C. Stadler, M. Odstrčil, E.H.R. Tsai, A. Diaz, M. Holler, I. Usov, J. Raabe, A. Menzel, M. Guizar-Sicairos, PtychoShelves, a versatile 
% high-level framework for high-performance analysis of ptychographic data, J. Appl. Cryst. 53(2) (2020). (doi: 10.1107/S1600576720001776)
% and 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 LSQ-ML:
% M. Odstrčil, A. Menzel, and M. Guizar-Sicairos, Iterative least-squares solver for generalized maximum-likelihood ptychography, Opt. Express 26(3), 3108 (2018). 
%   (doi: 10.1364/OE.26.003108),
% 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),
% and/or for OPRP:
% M. Odstrcil, P. Baksh, S. A. Boden, R. Card, J. E. Chad, J. G. Frey, W. S. Brocklesby,  Ptychographic coherent diffractive imaging with orthogonal probe relaxation. 
% Opt. Express 24.8 (8360-8369) 2016. (doi: 10.1364/OE.24.008360).
% 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 
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%       © 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 volData_upd = back_proj(projData_upd,theta,Npx_vol)
    
    projData_upd = gpuArray(projData_upd);  % difference after ptycho update 

    assert(isreal(projData_upd), 'Inputs are assumed to be real valued')
    
   
    
    Nlayers = size(projData_upd,3);   

    
    % permute to see it from the top direction 
    projData_upd = permute(projData_upd, [2,3,1]);
    
    % interpolate back to the full size 
    if Nlayers == 1
        % faster option for single layer 
        volData_upd = repmat(projData_upd* (Nlayers/Npx_vol(2)) ,[1,Npx_vol(2),1]);
    else
           
        
        %% periodic boundary 
        binning = ceil(Npx_vol(2)/Nlayers/4);  % in order to reduce computational requirements, use a combination of interpolation FFT and simple and fast upsampling
        Nl_upsample = Npx_vol(2) / binning; 
        assert(Nl_upsample == round(Nl_upsample), 'Volume size cannot be split for binning')
        % revert the 0.5px offset along the beam direction , process real and imag part separatelly
        % to avoid mixing 
             
        projData_upd = projData_upd * (Nlayers/Nl_upsample/binning); 
        
        %% %%% centered FFT interpolation %%%
        
        % pre-fft transform
        projData_upd = fft(projData_upd,[], 2);
        % apply 0.5 pixel shift 
        projData_upd = utils.imshift_fft_ax(projData_upd,0.5,2, false); 
        % interpolate to the full size 
        volData_upd = utils.interpolateFT_ax(projData_upd,Nl_upsample,2, false);
        % post-ifft transform
        volData_upd = real(ifft(volData_upd,[], 2));
        
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        
        % finally quickly upsample to the full required size  
        volData_upd = utils.unbinning_2D(volData_upd, [1, binning]);         
    end
     
    
    % back rotate to the basic orientation , use bilinear interpolation
    % because it is much faster than FFT rotation
    volData_upd = utils.imrotate_ax(volData_upd,  -theta, 3, 0, 'bicubic');
   
end