Iterative convex refinement for sparse recovery

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

    Research output: Contribution to journalArticle

    25 Citations (Scopus)

    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

    Fingerprint

    Refinement
    Recovery
    Optimization Problem
    Sparsity
    Convex optimization
    Image Recovery
    Nonconvex Problems
    Nonnegativity
    Experimental Validation
    Coefficient
    Synthetic Data
    Convex Optimization
    Spike
    Optimal Solution
    Regression
    Converge
    Alternatives
    Model

    All Science Journal Classification (ASJC) codes

    • Signal Processing
    • Electrical and Electronic Engineering
    • Applied Mathematics

    Cite this

    Mousavi, Hojjat S. ; Monga, Vishal ; Tran, Trac D. / Iterative convex refinement for sparse recovery. In: IEEE Signal Processing Letters. 2015 ; Vol. 22, No. 11. pp. 1903-1907.
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    Iterative convex refinement for sparse recovery. / Mousavi, Hojjat S.; Monga, Vishal; Tran, Trac D.

    In: IEEE Signal Processing Letters, Vol. 22, No. 11, 7114220, 01.11.2015, p. 1903-1907.

    Research output: Contribution to journalArticle

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