A Matching Pursuit Generalized Approximate Message Passing Algorithm

This paper proposes a novel matching pursuit generalized approximate message passing (MPGAMP) algorithm which explores the support of sparse representation coefficients step by step, and estimates the mean and variance of non-zero elements at each step based on a generalized-approximate-message-passing-like scheme. In contrast to the classic message passing based algorithms and matching pursuit based algorithms, our proposed algorithm saves a lot of intermediate process memory, and does not calculate the inverse matrix. Numerical experiments show that MPGAMP algorithm can recover a sparse signal from compressed sensing measurements very well, and maintain good performance even for non-zero mean projection matrix and strong correlated projection matrix.