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2026-09-17 21:49:08 +09:00 · 2026-08-07 15:56:42 +09:00
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+% INTERPOLATEFT_AX Computes interpolated array using 1D Fourier transform, i.e. dirichlet
+% interpolation along single axis. Computes the FT and then adjusts the size by zero padding
+% or cropping then it computes the IFT. A real valued input may have
+% residual imaginary components, which is given by numerical precision of
+% the FT and IFT.
+%
+% imout = interpolateFT_ax(im,outsize,ax, use_fft)
+%
+% Inputs:
+%   **im      - Input complex array
+%   **outsize - Output size of array [N pixels]
+%   **ax - index of axis along which interpolation is done 
+% *optional*
+%   **use_fft - if false, assume that im is already fft-transformed, default = true
+%
+% Outputs:
+%   ++imout   - Output complex image
+%
+% Example: 
+% x = randn(10,20,30); 
+% x_int = utils.interpolateFT_ax(x, 10, 3) % downsample to 10 pixels along 3rd axis 
+
+
+%*-----------------------------------------------------------------------*
+%|                                                                       |
+%|  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 [ imout ] = interpolateFT_ax(im,outsize,ax, use_fft)
+
+Nin = size(im);
+if ax > ndims(im)
+    Nin(ax) = 1; 
+end
+if nargin < 4
+    use_fft = true;
+end
+
+Nout = Nin;
+Nout(ax) = outsize;
+
+if use_fft
+    imFT = fft(im,[],ax);
+else
+    imFT = im; 
+end
+
+centerin = floor(Nin(ax)/2)+1;
+centerout = floor(Nout(ax)/2)+1;
+
+center_diff = centerout - centerin;
+
+
+grid_in = fftshift(1:Nin(ax)); 
+grid_in = grid_in(max(-center_diff+1,1):min(-center_diff+Nout(ax),Nin(ax)));
+grid_in = {grid_in,':',':',':'}; 
+grid_in = circshift( grid_in, ax-1); 
+
+grid_out = [max(ceil(Nout(ax)/2)+1,Nout(ax) - centerin+2):Nout(ax), ...
+            1:min(centerin-1, ceil(Nout(ax)/2))]; 
+grid_out = {grid_out,':',':',':'}; 
+grid_out = circshift( grid_out, ax-1); 
+
+
+
+if Nout(ax) > Nin(ax)
+    % perform multiplication to keep average values, 
+    % multiply the smaller array to save time 
+    imFT = imFT*(Nout(ax)/(Nin(ax)));
+end
+
+imout = zeros(Nout,'like',im);
+imout(grid_out{:}) = imFT(grid_in{:});
+
+
+if use_fft
+    imout = ifft(imout,[],ax);
+end
+
+if Nout(ax) < Nin(ax)
+    % perform multiplication to keep average values, 
+    % multiply the smaller array to save time 
+    imout = imout*(Nout(ax)/(Nin(ax)));
+end
+
+
+end