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+utils/interpolateFT_centered.m

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+% INTERPOLATEFT_CENTERED Perform FT interpolation of provided stack of images using FFT so that
+% the center of mass is not modified after the resolution change
+% This function is critical for subpixel accurate up/down sampling
+%
+% imout = interpolateFT_centered(im,downsample,interp_sign)
+%
+% Inputs:
+%   **im                - Input complex  2D array or stacked 3D array 
+%   **Npix_new          - (2x1 vector) Size of the interpolated array
+%   **interp_sign       - +1 or -1, sign that adds extra 1px shift. +1 is needed
+%                           if interpolation is used to downsample phase gradient which is used for
+%                           unwrapping, otherwise use -1
+% *returns*:
+%   ++imout   - Output complex image
+%
+
+
+%*-----------------------------------------------------------------------*
+%|                                                                       |
+%|  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 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 [ img ] = interpolateFT_centered(img,Np_new, interp_sign)
+    import utils.*
+    import math.*
+
+    Np = size(img); 
+    Np_new = 2+Np_new; 
+    isReal = isreal(img); 
+
+    scale = prod((Np_new-2)) / prod(Np(1:2));
+    downsample = ceil(sqrt(1/scale)); 
+
+    if isa(img, 'gpuArray')
+        scale = Garray(scale); 
+    end
+    % apply the padding to account for boundary issues 
+    img = padarray(img, double([downsample,downsample]), 'symmetric' ,'both'); 
+
+    % go to the fourier space 
+    img = fft2(img);
+
+    % apply +/-0.5 px shift
+    img = imshift_fft(img, interp_sign*-0.5, interp_sign*-0.5, false);
+
+    % crop in the Fourier space (can be speeded up similarly to example in utils.interpolateFT_ax )
+    img = ifftshift_2D(crop_pad(fftshift_2D(img), Np_new));
+
+    % apply -/+0.5 px shift in the cropped space 
+    img = imshift_fft(img,  interp_sign*0.5, interp_sign*0.5, false);
+
+    % return to the real space 
+    img = ifft2(img);
+
+    % scale to keep the average constant 
+    img = img*scale;
+
+    % remove the padding
+    img = img(2:end-1, 2:end-1,:); 
+
+    if isReal
+        img = real(img); % preserve complexity 
+    end
+end