Compressed Sensing via Sparse Bayesian Learning and Gibbs Sampling

Sparse Bayesian Learning (SBL) has been used as a sparse signal recovery algorithm for compressed sensing. It has been shown that SBL is easy to use and can recover sparse signals more accurately than the l ₁ based optimization approaches, which require a delicate choice of user parameters. We propose herein a modified Expectation Maximization (EM) based SBL algorithm referred to as SBL-alpha and a block Gibbs sampling algorithm referred to as BGS-alpha, both of which are based on a three-stage hierarchical Bayesian model. We compare both methods to a widely used benchmark SBL algorithm, which is equivalent to SBL-alpha with a = 0. We show that SBL-alpha with alpha = 1 not only is more accurate than the benchmark SBL algorithm in terms of the reconstruction error, but also converges faster. BGS-alpha with alpha = 1.5 is more accurate than SBL-1, but requires more computations.