% simple example (2D, single coil, no phase errors)
N = 256;
pf = 9/16; % a typical large partial fourier factor
p = single(phantom(N));
kspRef = fftshift(fftshift( fft(fft( fftshift(fftshift( p, 1),2), [],1),[],2), 1),2);
% kspRef = kspRef + 3 * complex( randn(N), randn(N) ); % add noise
kspPF = kspRef;
kspPF(:,1:floor((1-pf)*N)) = 0;
tmp = kspRef(:,end-floor((1-pf)*N)+1:end);
Res = kspRef(:,floor((1-pf)*N)+1:end);
B = conj(tmp);
C = flipud(B);
D = fliplr(C);
Y =[D,Res];
kspCS = Y;
imRef = ifftshift(ifftshift( ifft(ifft( ifftshift(ifftshift( kspRef, 1),2), [],1),[],2), 1),2);
imDirect = ifftshift(ifftshift( ifft(ifft( ifftshift(ifftshift( kspPF, 1),2), [],1),[],2), 1),2);
imCS = ifftshift(ifftshift( ifft(ifft( ifftshift(ifftshift( kspCS, 1),2), [],1),[],2), 1),2);
figure,
imagesc(abs([imRef imCS imDirect]), [0 2*mean(abs(imRef(:)))])
axis image
title('reference (full dataset) | conjugate symmetry | zero-padded reco')
colormap(gray(256))
The results show that “zero-filling" works better than " Conjugate Synthesis method" . What's wrong?
R. Allen Waggoner has post a perfect solution. But I just cannot understand why the center is not (128.5,128.5).
see the demonstration of symmetry:http://mri-q.com/phase-symmetry.html
http://mri-q.com/phase-symmetry.html