  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.
