Sparse Bayesian learning using approximate message passing

We use the approximate message passing framework (AMP) [1] to address the problem of recovering a sparse vector from undersampled noisy measurements. We propose an algorithm based on Sparse Bayesian learning (SBL) [2]. Unlike the original EM based SBL that requires matrix inversions, the proposed algorithm has linear complexity, which makes it well suited for large scale problems. Compared to other message passing techniques, the algorithm requires fewer approximations, due to the conditional Gaussian prior assumption on the original vector. Numerical results show that the proposed algorithm has comparable and in many cases better performance than existing algorithms despite significant reduction in complexity.