A GAMP Based Low Complexity Sparse Bayesian Learning Algorithm
This work addresses computational efficiency and robustness in sparse signal recovery for applications like compressed sensing, though it is incremental as it builds on existing GGAMP and SBL techniques.
The paper tackles sparse signal recovery by integrating damped Gaussian generalized approximate message passing (GGAMP) into sparse Bayesian learning (SBL), resulting in the GGAMP-SBL algorithm that is more robust to arbitrary measurement matrices and lower complexity than standard methods, with extensions to multiple measurement vectors (GGAMP-TSBL) and verification through numerical experiments.
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.