% 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

More Xiaolong Zhou's questions See All
Similar questions and discussions