While I can not comment on the content or merit of this work since I have not read the paper I can say that there is a lot of research going on in the area of MRI and a number of exciting things are happening. I work in a research group that works on impressive MRI techniques combined with algorithms that allow taking entire MRI movies (not just photographs). This is extremely interesting when looking at the beating human heart, speaking humans or moving joints. We are really just beginning to explore the potential this technology has for clinical applications. More information including impressive videos can be found here: http://en.wikipedia.org/wiki/Real-time_MRI.
The idea behind the extremely fast acquisition times is extreme under-sampling combined with iterative algorithms that are able to produce high quality images despite the incomplete measurements. This algorithms also exploit the fact that between two frames there is not a lot of change in the images since they are taken at time intervals of only dozens of ms. They are of course more complicated than simple fourier transforms as they model the acquisition process in more detail.
"If it's not loud, it doesn't work!" -- Blank Reg, from "Max Headroom"