Iterative convex refinement for sparse recovery

Hojjat S. Mousavi, Vishal Monga, Trac D. Tran

    Research output: Contribution to journalArticlepeer-review

    29 Scopus citations

    Abstract

    In this letter, we address sparse signal recovery in a Bayesian framework where sparsity is enforced on reconstruction coefficients via probabilistic priors. In particular, we focus on the setup of Yen who employ a variant of spike and slab prior to encourage sparsity. The optimization problem resulting from this model has broad applicability in recovery and regression problems and is known to be a hard non-convex problem whose 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.

    Original languageEnglish (US)
    Article number7114220
    Pages (from-to)1903-1907
    Number of pages5
    JournalIEEE Signal Processing Letters
    Volume22
    Issue number11
    DOIs
    StatePublished - Nov 1 2015

    All Science Journal Classification (ASJC) codes

    • Signal Processing
    • Electrical and Electronic Engineering
    • Applied Mathematics

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