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Inspired by the recently proposed Magnetic Resonance Fingerprintingtechnique, we develop a principled compressed sensing framework forquantitative MRI. The three key components are: a random pulse excitationsequence following the MRF technique; a random EPI subsampling strategy and aniterative projection algorithm that imposes consistency with the Blochequations. We show that, as long as the excitation sequence possesses anappropriate form of persistent excitation, we are able to achieve accuraterecovery of the proton density, $T_1$, $T_2$ and off-resonance mapssimultaneously from a limited number of samples.

Compressed Quantitative MRI: Bloch Response Recovery through Iterated Projection