  In this paper, we introduce a new sparsity-promoting prior, namely, the
"normal product" prior, and develop an efficient algorithm for sparse signal
recovery under the Bayesian framework. The normal product distribution is the
distribution of a product of two normally distributed variables with zero means
and possibly different variances. Like other sparsity-encouraging distributions
such as the Student's $t$-distribution, the normal product distribution has a
sharp peak at origin, which makes it a suitable prior to encourage sparse
solutions. A two-stage normal product-based hierarchical model is proposed. We
resort to the variational Bayesian (VB) method to perform the inference.
Simulations are conducted to illustrate the effectiveness of our proposed
algorithm as compared with other state-of-the-art compressed sensing
algorithms.
