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% [img_out, gamma,gamma_x, gamma_y, c_offset] = stabilize_phase(img, varargin)
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% Description: adjust phase of the object to be mostly around zero or close
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% to the provided reference image img_ref and remove linear ramp, phase
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% offset and if normalize_amplitude==true normalize amplitude to be around 1
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%
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% Method:
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% 1) if fourier_guess == true and remove_ramp == true, get rough estiamte of the center of FFT and
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% use it to subtract phase ramp, IT CAN FAIL IF SAMPLE HAS STRONG
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% AMPLITUDE AND PHASE VARIATION, IT IS NOT ABLE TO USE THE WEIGHTS
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% 2) if remove_ramp == true, accuratelly refine the phase ramp by weighted
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% LSQ method, regions were W is small have small importance in the phase
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% ramp estiamtion. SECOND STEP ASSUMES THAT THE PHASE RAMP IN IMAGE IS
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% SMALLER THAN 2PI ACROSS THE IMAGE
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%
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% Inputs:
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% **img_orig - complex image to stabilize
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% **img_ref - complex images used as reference, if empty ones is used
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% *optional*:
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% **weights - (array) 0<x<1 numeric array denoting reliable unwrapping region
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% **split - (int) split FFTon smaller blocks on GPU
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% **fourier_guess - (bool), use maximum in Fourier space to get initial guess of the phase ramp
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% **remove_ramp - (bool), if false, remove only phase offset (scalar)
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% **binning - (int) bin the array to speed up phase ramp calculation and make it more robust
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% **normalize_amplitude - (bool) normalize amplitude to have average value around one
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% **split - (scalar) split volume, important for GPU when fft of large array is calculated
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%
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% returns:
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% ++img_out - phase ramp / offset subtracted complex-valued image
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% ++gamma,gamma_x, gamma_y - (1,1,N arrays) offset, ramp horizontal / vertical
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% ++c_offset - 2D/3D array - either constant or phase ramp offset subtracted directly from the
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% complex data as img .* exp(1i*c_offset)
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%
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% Example how to correct output image using gamma,gamma_x, gamma_y
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% [M0, N0] = size(img_orig);
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% c_offset = angle(gamma) + xramp.*gamma_x*M0 + yramp.*gamma_y*N0;
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% img_out = img_orig.*exp(1i*c_offset);
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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_out, gamma,gamma_x, gamma_y, c_offset] = stabilize_phase(img_orig, varargin)
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import math.*
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import utils.*
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par = inputParser;
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par.addOptional('img_ref', [] )
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par.addOptional('weights', [] )
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par.addParameter('fourier_guess', true , @islogical ) % use cross correlation as initial guess, avoids local minima but can be dangerous
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par.addParameter('remove_ramp', true , @islogical ) % remove also ramp, not only offset
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par.addParameter('binning', 0, @isint ) % bin the array to speed up phase ramp calculation
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par.addParameter('normalize_amplitude', false, @islogical )% normalize amplitude to have average value around one
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par.addParameter('split', 1, @isnumeric ) % split volume, important for GPU when fft of large array is calculated
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par.parse(varargin{:})
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r = par.Results;
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img_ref = r.img_ref;
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weights = r.weights;
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binning = max(1, r.binning);
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[M0,N0,~] = size(img_orig);
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if isreal(img_orig)
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return % if the input is real, no phase shift is needed
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end
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if isempty(img_ref)
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img_ref = 1;
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end
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if isempty(weights)
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weights = 1;
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end
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if isvector(img_orig)
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%% calculate the optimal phase shift
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gamma = mean2(img_ref .* conj(img_orig));
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gamma = gamma./abs(gamma);
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if isnan(gamma); gamma = 1; end
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img_out = img_orig * gamma;
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return
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end
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img = img_orig;
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if binning > 1
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% speed up calculation and make more robust by binning
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img = utils.binning_2D(img, binning);
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if ~isscalar(img_ref) || isempty(img_ref)
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img_ref= utils.binning_2D(img_ref, binning);
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end
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if ~isscalar(weights) || isempty(weights)
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weights= utils.binning_2D(weights, binning);
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end
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end
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%% calculate complex phase difference
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phase_diff = img_ref .* conj(img);
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[M,N,~] = size(img);
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xramp = pi*(linspace(-1,1,M))';
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yramp = pi*(linspace(-1,1,N));
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if r.fourier_guess && r.remove_ramp
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%% initial guess based on position of maximum in Fourier domain
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xcorrmat = ifftshift_2D(abs(ifft2_partial((phase_diff), r.split))).^2;
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% center of mass seems to be more accurate if the phase FFT has bimodal distribution, now I
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% take center of mass of regions > 0.5 of xcorr maximum
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[y,x] = center(max(0,xcorrmat-max(max(xcorrmat))/2), false);
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x=x-ceil(M/2)-1;
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y=y-ceil(N/2)-1;
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c_offset = xramp.*x + yramp.*y;
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phase_diff = phase_diff.*exp(1i*c_offset);
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end
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%% calculate the optimal phase shift
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gamma = mean2(phase_diff .*weights) ./ mean2(weights);
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gamma = gamma./abs(gamma);
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if any(isnan(gamma)); gamma = 1; end
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if r.remove_ramp
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phase_diff = phase_diff .* conj(gamma);
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%% linear refinement
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phase_diff= angle(phase_diff).*weights; % linearize the problem
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gamma_x=mean2(phase_diff.*xramp) ./ mean2(weights.*abs(xramp).^2);
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gamma_y=mean2(phase_diff.*yramp) ./ mean2(weights.*abs(yramp).^2);
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if r.fourier_guess
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%% get total correction
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gamma_x = gamma_x - x;
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gamma_y = gamma_y - y;
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end
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% export dimensionless
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gamma_x = gamma_x / M;
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gamma_y = gamma_y / N;
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%% correct output image
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xramp = pi*(linspace(-1,1,M0))';
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yramp = pi*(linspace(-1,1,N0));
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if isa(img_orig, 'gpuArray')
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xramp = gpuArray(xramp);
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yramp = gpuArray(yramp);
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[img_out,c_offset] = arrayfun(@remove_phase,img_orig, xramp, yramp, gamma, gamma_x*M0/binning, gamma_y*N0/binning);
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else
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[img_out,c_offset] = remove_phase(img_orig, xramp, yramp, gamma, gamma_x*M0/binning, gamma_y*N0/binning);
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end
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else
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img_out = img_orig .* gamma;
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c_offset = angle(gamma);
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end
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if r.normalize_amplitude
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mean_amplitude = mean2(weights .* img_out) ./ mean2(weights);
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img_out = img_out ./ mean_amplitude;
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end
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end
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% auxiliar function for GPU processing (kernel merging)
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function [img_out,c_offset] = remove_phase(img_orig, xramp, yramp, gamma, gamma_x, gamma_y)
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%% correct output image
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c_offset = angle(gamma) + xramp.*gamma_x + yramp.*gamma_y;
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img_out = img_orig.*exp(1i*c_offset);
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end
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