An Expectation Propagation Perspective on Approximate Message Passing

An alternative derivation for the well-known approximate message passing (AMP) algorithm proposed by Donoho et al. is presented in this letter. Compared with the original derivation, which exploits central limit theorem and Taylor expansion to simplify belief propagation (BP), our derivation resorts to expectation propagation (EP) and the neglect of high-order terms in large system limit. This alternative derivation leads to a different yet provably equivalent form of message passing, which explicitly establishes the intrinsic connection between AMP and EP, thereby offering some new insights in the understanding and improvement of AMP.