  Sparse Bayesian learning (SBL) is a popular approach to sparse signal
recovery in compressed sensing (CS). In SBL, the signal sparsity information is
exploited by assuming a sparsity-inducing prior for the signal that is then
estimated using Bayesian inference. In this paper, a new sparsity-inducing
prior is introduced and efficient algorithms are developed for signal recovery.
The main algorithm is shown to produce a sparser solution than existing SBL
methods while preserving their desirable properties. Numerical simulations with
one-dimensional synthetic signals and two-dimensional images verify our
analysis and show that for sparse signals the proposed algorithm outperforms
its SBL peers in both the signal recovery accuracy and computational speed. Its
improved performance is also demonstrated in comparison with other
state-of-the-art methods in CS.
