  Inspired by the recently proposed Magnetic Resonance Fingerprinting (MRF)
technique, we develop a principled compressed sensing framework for
quantitative MRI. The three key components 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 theoretically, as long as the excitation sequence
possesses an appropriate form of persistent excitation, we are able to
accurately recover the proton density, T1, T2 and off-resonance maps
simultaneously from a limited number of samples. These results are further
supported through extensive simulations using a brain phantom.
