inverse fast-fourier transformation in mri

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

Answer 1

[Gargi Patil]

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');

[Mehri Mehrnia]

why you have used (log(1+abs()) for fftshow?

Answer 2

[William Ngaleu]

Thanks for your respond. But the problem is: by programming i don't have the variable "fftimage". I have got the kspace through other transformations and i want to "reconstruct" (or construct) the image from that kspace. To resume i want to do the ifft of the kspace without having an initial image.

[Gargi Patil]

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]

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)));