A New and Robust AMP Algorithm for Non IID Matrices Based on Bayesian Theory in Compressed Sensing

AMP is a low-cost iterative algorithm for recovering signal in compressed sensing. When the sampling matrix has IID zero-mean Gaussian elements, the convergence of AMP is analytically guaranteed. But for other sampling matrices, especially ill-conditioned matrices, the recovery performance of AMP degrades and even may be diverged. This problem limits the use of AMP in some applications such as imaging. In this paper, a method is proposed for modifying the AMP algorithm based on Bayesian theory for non-IID matrices. Simulation results show better robustness properties of the proposed algorithm for non-IID matrices in comparison with previous works. In other words, the proposed method has more precision in recovery, and converges with less iterations.