Broken MRI

The questions below are due on Thursday May 08, 2025; 02:00:00 PM.
 
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Plotted below is the absolute value of the k-space data (left) from an MRI and the absolute value of the reconstructed image (right).

Consider the scenario that while the MRI data are being collected, there are perturbations, and as a result, the k-space data are distorted. In this problem, we model these perturbations as multiplications with sine^2 or cosine^2 of k_r or k_c. Below are several k-space images that have been distorted in this way. In all cases, assume that only the magnitude of the k-space data was changed.

Match each k-space image with the corresponding reconstructed spatial-domain image, and enter your results below.

k-space A:

matching reconstructed image:

k-space B:

matching reconstructed image:

k-space C:

matching reconstructed image:

k-space D:

matching reconstructed image:

k-space E:

matching reconstructed image:

k-space F:

matching reconstructed image:

 

 

y_{1}[r, c] y_{2}[r, c] y_{3}[r, c]
     
y_{4}[r, c] y_{5}[r, c] y_{6}[r, c]
     
y_{7}[r, c] y_{8}[r, c] y_{9}[r, c]
     
y_{10}[r, c] y_{11}[r, c] y_{12}[r, c]