# Question about MRI signal construction

As I understand it, in MRI, a line in k-space is usually acquired while the readout gradient is applied. So during the application of this gradient the protons spin at different frequencies along the gradient.

Now, I sample the MRI signal during the application of this gradient. My confusion is that I can sample the signal at arbitrary resolution and the inverse FFT will produce the image with as many pixels as the sampling resolution.

To make the question a bit concrete. let's say I have simulated 128 spins at a distance of 1 mm apart. This will give me an object with the FOV of 0.128 meters.

Now say during the readout I sample 10000 equidistant points. So, effectively I have collected 10000 complex k-space values. An inverse FFT would also give me an image with 10000 pixels. Now, how do I resolve this 10000 pixel image into a 128 pixel image where each pixel corresponds to the corresponding spin.