Paper Info
Title
Iterative Convex Refinement For Sparse Recovery
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 et al. [29] 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.
Year
DOI
Venue
2015
10.1109/LSP.2015.2438255
IEEE SIGNAL PROCESSING LETTERS
Keywords
Field
DocType
Bayesian inference, compressive sensing, image reconstruction, optimization, sparse recovery, spike and slab prior
Iterative reconstruction,Mathematical optimization,Pattern recognition,Sparse approximation,Synthetic data,Artificial intelligence,Probabilistic logic,Prior probability,Optimization problem,Convex optimization,Mathematics,Linear matrix inequality
Journal
Volume
Issue
ISSN
22
11
1070-9908
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Hojjat Seyed Mousavi1684.29
Vishal Monga267957.73
Trac D. Tran31507108.22