Sparse signal recovery using generalized approximate message passing with built-in parameter estimation

Abstract

The generalized approximate message passing (GAMP) algorithm under the Bayesian setting shows significant advantages in recovering under-sampled sparse signals from corrupted observations. Compared to conventional convex optimization methods, it has a much lower complexity and is computationally tractable. Under the GAMP framework, the sparse signal and the observation are viewed to be generated according to some pre-specified probability distributions in the input and output channels. However, the parameters of the distributions are usually unknown in practice and need to be decided. In this paper, we propose an extended GAMP algorithm with built-in parameter estimation (PE-GAMP). Specifically, PE-GAMP treats the parameters as unknown random variables with simple priors and jointly estimates them with the sparse signals along the recovery process. Sparse signal recovery experiments confirm PE-GAMP's convergence behavior and show that its performance matches the oracle GAMP algorithm that has the knowledge of the true parameter values.