ICR: Iterative Convex Refinement for Sparse Signal Recovery Using Spike and Slab Priors
This addresses sparse signal recovery for applications like image processing, but it appears incremental as it builds on existing Bayesian frameworks with a new optimization approach.
The paper tackles sparse signal recovery using spike and slab priors by proposing Iterative Convex Refinement (ICR), which solves a sequence of convex problems to converge to a sub-optimal solution, and shows experimental validation on synthetic and real-world image data with merits over state-of-the-art alternatives.
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.