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% IMRESCALE_FRFT subpixel accurate image rescaling based on fractional fourier
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% transformation (FRFT)
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%
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% img = imrescale_frft(img, scale_x, scale_y, scale_z)
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%
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% Inputs:
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% **img 2D or stack of 2D images
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% **scale_x - horizontal scaling factor
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% *optional*
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% **scale_y - vertical scaling factor, if not provided scale_x is used
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% **scale_z - 3rd axis scaling factor, if not provided, no scaling is
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% used along 3rd axis
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% *returns*:
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% ++img 2D or stack of 2D images scaled by factors scale_x, (scale_y)
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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 following 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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% computing language 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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% computing language the authors and institution should be acknowledged
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% in written form in the publication: “Data processing was carried out
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% using 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 describing features, or parameters, that
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% are already existing 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 [img, win] = imrescale_frft(img, scale_x, scale_y, scale_z)
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isReal = isreal(img);
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win = [];
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if ~isvector(scale_x) && ~isscalar(scale_x)
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error('Inputs scaling is expected as scalar or vector')
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end
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if nargin < 3 && (size(img,1)==size(img,2))
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% 2d version is faster only for many stacked pictures
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if scale_x > 1
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win = get_window(img, scale_x, 1) .* get_window(img, scale_x, 2);
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img = img .* win;
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end
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%size(img)
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img = math.fftshift_2D(ifft2(math.fftshift_2D(FRFT_2D(img,scale_x))));
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else
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if nargin < 3
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scale_y = scale_x;
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end
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if any(scale_y ~= 1)
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img = math.fftshift_2D(ifft(math.fftshift_2D(FRFT_1D(img,scale_y))));
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end
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if any(scale_x ~= 1)
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img = permute(img,[2,1,3]);
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img = math.fftshift_2D(ifft(math.fftshift_2D(FRFT_1D(img,scale_x))));
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img = permute(img,[2,1,3]);
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end
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if nargin > 3
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if any(scale_z ~= 1)
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img = permute(img,[3,2,1]);
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img = math.fftshift_2D(ifft(math.fftshift_2D(FRFT_1D(img,scale_z))));
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img = permute(img,[3,2,1]);
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end
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end
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end
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if isReal
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img = real(img);
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end
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end
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function win = get_window(img, scale, ax)
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% apodize window for img to prevent periodic boundary errors
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win = ones(ceil(size(img,ax)/scale/2)*2,class(img));
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win = utils.crop_pad(win, [size(img,ax),1]);
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win = shiftdim(win, 1-ax);
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end
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function X=FRFT_1D(X,alpha)
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% 1D fractional fourier transformation
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% See A. Averbuch, "Fast and Accurate Polar Fourier Transform"
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%% it works as magnification lens Claus, D., & Rodenburg, J. M. (2015). Pixel size adjustment in coherent diffractive imaging within the Rayleigh–Sommerfeld regime
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%% test plot(abs(fftshift(ifft((FRFT_1D(x,scale))))))
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N = size(X,1);
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grid = fftshift(-N:N-1)';
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preFactor = reshape(exp(1i*pi*grid*alpha(:)'),2*N,1,[]); % perform shift
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Factor= reshape(exp(-1i*pi*grid.^2/N * alpha(:)'),2*N,1,[]); % propagation / scaling
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X=[X; zeros(size(X), class(X))]; % add oversampling
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X= bsxfun(@times, X, Factor .* preFactor);
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% avoid duplication of XX
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X=fft(X);
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X = bsxfun(@times, X,fft(conj(Factor)));
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X=ifft(X);
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X=bsxfun(@times, X,reshape(Factor .* preFactor,2*N,1,[]));
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X=X(1:N,:,:);
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%% remove phase offset
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X = bsxfun(@times, X , reshape(exp(-1i*pi*N*alpha/2),1,1,[]));
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end
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function X=FRFT_2D(X,alpha)
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% 2D fractional fourier transformation
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% See A. Averbuch, "Fast and Accurate Polar Fourier Transform"
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%% it maybe works as magification lens Claus, D., & Rodenburg, J. M. (2015). Pixel size adjustment in coherent diffractive imaging within the Rayleigh–Sommerfeld regime
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alpha = reshape(alpha,1,1,[]);
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N = size(X,1);
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grid = (fftshift(-N:N-1)') * ones(1, 'like', X);
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[Xg,Yg] = meshgrid(grid(1:N), grid(1:N));
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preFactor = exp((1i*pi.*alpha)*(-N/2+(Xg+Yg) - (1/N)*(Xg.^2+Yg.^2))); % perform shift after FFT
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[Xg,Yg] = meshgrid(grid, grid);
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Factor=exp((1i*pi/N(1))*(Xg.^2+Yg.^2) .* alpha); % propagation / scaling
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Factor = fft2(Factor);
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X= X .* preFactor;
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if length(size(X))==4 %%added by YJ to present errors when using variable probe
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x_tilde = zeros(2*N, 2*N, size(X,3), size(X,4), 'like', X);
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% upsample the X array
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x_tilde(1:N, 1:N,:,:) = X;
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X=fft2(x_tilde);
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X = X .* Factor;
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X=ifft2( X );
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X=X(1:N,1:N,:,:);
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else %%length(size(X))==3
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x_tilde = zeros(2*N, 2*N, size(X,3), 'like', X);
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% upsample the X array
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x_tilde(1:N, 1:N,:) = X;
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X=fft2(x_tilde);
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X = X .* Factor;
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X=ifft2( X );
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X=X(1:N,1:N,:);
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end
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X=X.* preFactor;
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end
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