Fast Bayesian Signal Recovery in Compressed Sensing with Partially Unknown Discrete Prior

Bayesian Approximate Message Passing (BAMP) provides excellent recovery performance in Compressed Sensing (CS), but one seemingly needs to know the pdf of the signal prior. If the shape of the pdf is known but not its parameters, we show how they can be estimated with very low complexity during the BAMP iterations by the well-known Method of Moments (MoM). We compare the new approach with an established scheme from the literature that is based on the Expectation Maximization (EM) algorithm. By simulations we show that the MoM-based BAMP scheme works at least as good as the EM-based approach and with much lower complexity.