Abstract: From a Bayesian perspective, the commonly used sparse recovery algorithms, including Sparse Bayesian Learning (SBL), Regularized FOCUSS (R_FOCUSS) and Log-Sum, are compared. The analysis shows that, as a special case of latent variable Bayesian models, SBL, which operates in latent variable space via type-II maximum likelihood method, can be viewed as a more general and flexible means, and offers an avenue for improvement when finding sparse solutions to underdetermined inverse problems. Numerical results demonstrate the superior performance of SBL as compared to state-of-the-art sparse methods based on type-I maximum likelihood.