  In this letter, we address sparse signal recovery using spike and slab
priors. In particular, we focus on a Bayesian framework where sparsity is
enforced on reconstruction coefficients via probabilistic priors. The
optimization resulting from spike and slab prior maximization is known to be a
hard non-convex problem, and existing solutions involve simplifying assumptions
and/or relaxations. We propose an approach called Iterative Convex Refinement
(ICR) that aims to solve the aforementioned optimization problem directly
allowing for greater generality in the sparse structure. Essentially, ICR
solves a sequence of convex optimization problems such that sequence of
solutions converges to a sub-optimal solution of the original hard optimization
problem. We propose two versions of our algorithm: a.) an unconstrained
version, and b.) with a non-negativity constraint on sparse coefficients, which
may be required in some real-world problems. Experimental validation is
performed on both synthetic data and for a real-world image recovery problem,
which illustrates merits of ICR over state of the art alternatives.
