# A GAMP Based Low Complexity Sparse Bayesian Learning Algorithm

arXiv: https://arxiv.org/abs/1703.03044 · HTML: https://mlsanity.com/paper/1703.03044/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2017.

## Built on by (most cited first, 6 of 6)

- [Covariance-Free Sparse Bayesian Learning](https://mlsanity.com/paper/2105.10439/) (2021)
- [High-Dimensional Sparse Bayesian Learning without Covariance Matrices](https://mlsanity.com/paper/2202.12808/) (2022)
- [Efficient Network Automatic Relevance Determination](https://mlsanity.com/paper/2506.12352/) (2025)
- [Complexity-Optimized Sparse Bayesian Learning for Scalable Classification Tasks](https://mlsanity.com/paper/2107.08195/) (2021)
- [A Unitary Transform Based Generalized Approximate Message Passing](https://mlsanity.com/paper/2210.08861/) (2022)
- [Signal Recovery Using a Spiked Mixture Model](https://mlsanity.com/paper/2501.01840/) (2025)

## Abstract (arXiv)

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 boldsymbolA 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.