Inspired by the recently proposed Magnetic Resonance Fin- gerprinting technique, we develop a principled compressed sensing framework for quantitative MRI. The three key com- ponents are: a random pulse excitation sequence following the MRF technique; a random EPI subsampling strategy and an iterative projection algorithm that imposes consistency with the Bloch equations. We show that, as long as the ex- citation sequence possesses an appropriate form of persistent excitation, we are able to achieve accurate recovery of the proton density, T1, T2 and off-resonance maps simultane- ously from a limited number of samples.