Broken MRI

The questions below are due on Thursday December 04, 2025; 02:00:00 PM.
 
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The left image below shows the magnitude of the k-space data obtained for an MRI, and the right image shows the reconstructed image.

Consider how the image would change if the k-space data were multiplied by \sin^2(\cdot) or \cos^2(\cdot) of k_r or k_c. Below are several k-space representations that have been distorted in this way. In each case, assume that only the magnitude of the k-space data is changed. Match each k-space image with the corresponding reconstructed image, and enter your results from the corresponding pull-down list.

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]