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This paper considers the fundamental limit of compressed sensing for i.i.d.signal distributions and i.i.d. Gaussian measurement matrices. Its maincontribution is a rigorous characterization of the asymptotic mutualinformation (MI) and minimum mean-square error (MMSE) in this setting. Undermild technical conditions, our results show that the limiting MI and MMSE areequal to the values predicted by the replica method from statistical physics.This resolves a well-known problem that has remained open for over a decade.

The Replica-Symmetric Prediction for Compressed Sensing with Gaussian Matrices is Exact