# A GAMP Based Low Complexity Sparse Bayesian Learning Algorithm

## TL;DR

This paper introduces a low-complexity, robust sparse Bayesian learning algorithm using GGAMP within EM, extending from single to multiple measurement vectors, with verified efficiency and robustness.

## Contribution

It presents a novel GGAMP-based SBL algorithm that reduces complexity and improves robustness, extending to temporally correlated MMV scenarios.

## Key findings

- Algorithm is more robust to arbitrary measurement matrices.
- Significant reduction in computational complexity.
- Numerical experiments confirm robustness and efficiency.

## 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 $\boldsymbol{A}$ 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.