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% [PSD, freq] = power_spectral_density(img, varargin)
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% Computes the power spectral density of the provided 3D image.
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% Can handle non-cube arrays but assumes the voxel is isotropic
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%
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% Inputs:
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% img input image (2D or 3D)
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%
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% Parameters:
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% thickring Normally the pixels get assigned to the closest integer pixel ring in Fourier domain.
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% With thickring the thickness of the rings is increased by
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% thickring, so each ring gets more pixels and more statistics
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% auto_binning apply binning if dimensions are significanlty different along each axis
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% mask bool array equal to false for ignored pixels of the fft space
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%
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% Outputs:
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% PSD PSD curve values
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% freq normalized spatial frequencies to 1
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%
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% Example of use:
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% img = randn(512,512,512);
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% utils.power_spectral_density(img, 'thickring', 3);
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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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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function [PSD, freq] = power_spectral_density(img, air, varargin)
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import math.isint
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import utils.*
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%%%%%%%%%%%%%%%%%%%%% PROCESS PARAMETERS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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parser = inputParser;
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parser.addParameter('thickring', 3 , @isnumeric ) % thick ring in Fourier domain
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parser.addParameter('auto_binning', true , @islogical ) % bin FRC before calculating rings, it makes calculations faster
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parser.addParameter('max_rings', 200 , @isnumeric ) % maximal number of rings if autobinning is used
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parser.addParameter('mask', true, @islogical ) % bool array, equal to false for ignored pixels of the fft space
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parser.addParameter('windowautopos', true, @islogical ) % automatically position plotted window
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parser.addParameter('figure_id', 101, @isint) % call figure(figure_id)
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parser.parse(varargin{:})
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param = parser.Results;
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disp('Calculating PSD');
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% remove masked values from consideration (i.e. for laminography)
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Fimg = abs(bsxfun(@times,fftn(img) , param.mask+eps)).^2;
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[ny,nx,nz] = size(img);
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nmin = min(size(img));
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% avoid edge artefacts
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img = img .* tukeywin(size(img,1),0.5) .* tukeywin(size(img,2),0.5)' .* reshape(tukeywin(size(img,3),0.5),1,1,[]);
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thickring = param.thickring;
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if param.auto_binning
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% bin the correlation values to speed up the following calculations
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% find optimal binning to make the volumes roughly cubic
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bin = ceil(thickring/4) * floor(size(img)/ nmin);
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% avoid too large number of rings
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bin = max(bin, floor(nmin ./ param.max_rings));
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if any(bin > 1)
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fprintf('Autobinning %ix%ix%i \n', bin)
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thickring = ceil(thickring / min(bin));
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% fftshift and crop the arrays to make their size dividable by binning number
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if ismatrix(img); bin(3) = 1; end
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% force the binning to be centered
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subgrid = {fftshift(ceil(bin(1)/2):(floor(ny/bin(1))*bin(1)-floor(bin(1)/2)-1)), ...
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fftshift(ceil(bin(2)/2):(floor(nx/bin(2))*bin(2)-floor(bin(2)/2)-1)), ...
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fftshift(ceil(bin(3)/2):(floor(nz/bin(3))*bin(3)-floor(bin(3)/2)-1))};
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if ismatrix(img); subgrid(3) = [] ; end
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% binning makes the shell / ring calculations much faster
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Fimg = ifftshift(utils.binning_3D(Fimg(subgrid{:}), bin));
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end
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else
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bin = 1;
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end
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[ny,nx,nz] = size(Fimg);
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nmax = max([nx ny nz]);
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nmin = min(size(img));
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% empirically tested that thickring should be >=3 along the smallest axis to avoid FRC undesampling
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thickring = max(thickring, ceil(nmax/nmin));
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param.thickring = thickring;
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rnyquist = floor(nmax/2);
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freq = [0:rnyquist];
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x = ifftshift([-fix(nx/2):ceil(nx/2)-1])*floor(nmax/2)/floor(nx/2);
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y = ifftshift([-fix(ny/2):ceil(ny/2)-1])*floor(nmax/2)/floor(ny/2);
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if nz ~= 1
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z = ifftshift([-fix(nz/2):ceil(nz/2)-1])*floor(nmax/2)/floor(nz/2);
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else
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z = 0;
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end
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[X,Y,Z] = meshgrid(single(x),single(y),single(z));
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index = (sqrt(X.^2+Y.^2+Z.^2));
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clear X Y Z
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Nr = length(freq);
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for ii = 1:Nr
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r = freq(ii);
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progressbar(ii,Nr)
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% calculate always thickring, min ring thickness is given by the smallest axis
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ind = index>=r-thickring/2 & index<=r+thickring/2 ;
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ind = find(ind); % find seems to be faster then indexing
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auxFimg = Fimg(ind);
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C(ii) = sum(auxFimg);
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n(ii) = numel(ind); % Number of points
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end
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n = n*prod(bin); % account for larger number of elements in the binned voxels
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PSD = abs(C) ./ n;
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freq = freq/freq(end);
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figure(param.figure_id)
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hold all
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plot(freq, PSD)
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hold off
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set(gca, 'yscale', 'log')
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ylabel('Power spectral density')
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xlabel('Spatial frequency/Nyquist')
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grid on
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end
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