Efficient sparse Bayesian learning via Gibbs sampling

Sparse Bayesian learning (SBL) has been used as a 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 well-known Basis Pursuit (BP) algorithm. However, the computational complexity of SBL is quite high, which limits its use in large-scale problems. We propose herein an efficient Gibbs sampling approach, referred to as GS-SBL, for compressed sensing. Numerical examples show that GS-SBL can be faster and perform better than the existing SBL approaches.