His work on compressed sensing is ground-breaking, seriously game-changing stuff. Full-fidelity reconstruction of a data set from sub-Nyquist sampling through the use of a priori information about the data set's properties in some sparse representation... brilliant!
I've only heard of him from his comments on rjlipton's blog posts about the claimed P != NP proof, but from just that it's clear that he's a good communicator on top of being a math genius.