Rigorous Dynamics of Expectation-Propagation-Based Signal Recovery from Unitarily Invariant Measurements

Abstract: This paper investigates sparse signal recovery based on expectation propagation (EP) from unitarily invariant measurements. A rigorous analysis is presented for the state evolution (SE) of an EP-based message-passing algorithm in the large system limit, where both input and output dimensions tend to infinity at an identical speed. The main result is the justification of an SE formula conjectured by Ma and Ping.