inverse fast-fourier transformation in mri
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Hello dear MATLB users,
i have some problem regarding the ifft in the mri and it would be great if someone could help me. The fact is: i want to move from k-space to the image space using the ifft. I have tried to apply it but it unfortunately doesn't work. Youn could find how my kspace looks like in the attached file.
Thanks.
William
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Answers (2)
Gargi Patil
on 3 Sep 2021
Hi,
To find the inverse Fourier transform of an image, I'd recommend using the function ifft2. You can refer to the following code demonstrating the workflow to find the fft and ifft of a demo MATLAB image:
i = imread('peppers.png');
subplot(1,3,1)
imshow(i);
title('Original Image');
%Find fft of image
grayi = rgb2gray(i);
fftimage = fftshift(fft2(grayi));
subplot(1,3,2)
fftshow = mat2gray(log(1+abs(fftimage)));
imshow(fftshow)
title('FFT of Image');
%Take ifft of image
inverse = abs(ifft2(fftimage));
inverse = mat2gray(inverse);
subplot(1,3,3)
imshow(inverse);
title('IFFT of Image');
1 Comment
William Ngaleu
on 6 Sep 2021
2 Comments
Gargi Patil
on 6 Sep 2021
Hi William,
To obtain the original image, the code to find the ifft of an image can be referred to:
%Take ifft of image
inverse = abs(ifft2(kpsaceImage));
inverse = mat2gray(inverse);
Here the variable kspaceImage refers to the image in the file attached to the question.
Johannes Fischer
on 13 Sep 2021
Remeber to apply fftshift also before the Fourier transform. Matlab assumes that the low frequencies are in the 'top left' corner of your matrix. If you ignore this, your phase information will be wrong. In the kSpace you show, kSpace center is actually in the middle of the matrix.
imageSpace = fftshift(ifft2(fftshift(kSpace)));
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