A GAMP Based Low Complexity Sparse Bayesian Learning Algorithm

Abstract--In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into Expectation-Maximization (EM)-based sparse Bayesian learning (SBL). In particular, GGAMP is used to implement the E-step in SBL in place of matrix inversion, leveraging the fact that GGAMP is guaranteed to converge with appropriate damping. The resulting GGAMP-SBL algorithm is much more robust to arbitrary measurement matrix A than the standard damped GAMP algorithm while being much lower complexity than the standard SBL algorithm. We then extend the approach from the single measurement vector (SMV) case to the temporally correlated multiple measurement vector (MMV) case, leading to the GGAMP-TSBL algorithm. We verify the robustness and computational advantages of the proposed algorithms through numerical experiments. The problem of sparse signal recovery (SSR) and the related problem of compressed sensing have received much attention in recent years [1]-[6]. Despite the difficulty in solving this problem [7], an important finding in recent years is that for a sufficiently sparse x and a well designed A, accurate recovery is possible by techniques such as basis pursuit and orthogonal matching pursuit [8]- [10]. The SSR problem has seen considerable advances on the algorithmic front and they include iteratively reweighted algorithms [11]-[13] and Bayesian techniques [14]-[20], among others. Two Bayesian techniques related to this work are the generalized approximate message passing (GAMP) and the sparse Bayesian learning (SBL) algorithms.