Robust Approximate Message Passing for Nonzero-mean Sensing Matrices

Abstract

The standard Approximate Message Passing (AMP) algorithm efficiently recovers a sparse signal from a small number of noisy linear measurements. It requires the measurement matrix to be zero-mean, however. Even small deviations from this requirement cause it to diverge. In this paper, we show how mean-removal can be combined with standard Bayesian AMP to achieve signal recovery. Furthermore, a modified Bayesian AMP algorithm is presented, which achieves performance comparable to AMP in the zero-mean measurement matrix regime even for large mean. Simulation results and state evolution for both techniques are provided.