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 $\mathbf{A}$ 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.

References in corpus (8)

• Sparse Signal Recovery with Temporally Correlated Source Vectors Using Sparse Bayesian Learning
• The dynamics of message passing on dense graphs, with applications to compressed sensing
• Expectation-Maximization Gaussian-Mixture Approximate Message Passing
• Efficient High-Dimensional Inference in the Multiple Measurement Vector Problem
• Adaptive Damping and Mean Removal for the Generalized Approximate Message Passing Algorithm
• Type I and Type II Bayesian Methods for Sparse Signal Recovery using Scale Mixtures
• On Convergence of Approximate Message Passing
• Sparse Estimation using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models

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