MRI K-space to image: why track frequencies in two dimensions? While trying to better understand how an MRI goes from k-space to an image, I came across this wonderful website that explains how you would represent an image as a collection of rows of pixels  where each row of pixels is represented as a sum of waves of greyscale intensity.
First you select a single row from an image.

Then you apply the Fourier transform to represent the row as a collection of waves.

What I don't understand is, if we can get the frequencies for each row and accurately reconstruct what a row of the image looks like via frequency encoding, and if we already know where each row is in relation to the other rows (position of the blue line), why do we need to do the same basic thing along a different dimension (the y-axis using phase encoding)? Isn't it sufficient to simply stack the rows to get the full image?
in MRI, you don't start with the image as pixels in spatial domain, but with the k-space data!
So, you don't &quot;construct k-space from the image&quot;, you &quot;construct the image from k-space&quot;, which takes a 2D inverse Fourier transform.
And that's not &quot;do it row-by-row&quot;; that is &quot;do it on all rows, then all columns of the result&quot;.