FYI:

The publication [1] that improved on the MRI results was the famous paper that layed out the foundation of the what is called "Compressed sampling" / "Compressive sensing". This is the main field of research for Signal Processing folks since around 2006. (Before it was mostly "just" Wavelets for a few decades).

In MRI you sample in the frequency domain (FFT) and compressive sensing can be used since MRI signals (which are structured signals) are sparse in that domain.

[1] Stable signal recovery from incomplete and inaccurate measurements