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 language | English (US) |
|---|---|
| Article number | 7114220 |
| Pages (from-to) | 1903-1907 |
| Number of pages | 5 |
| Journal | IEEE Signal Processing Letters |
| Volume | 22 |
| Issue number | 11 |
| DOIs | |
| State | Published - Nov 1 2015 |
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All Science Journal Classification (ASJC) codes
- Signal Processing
- Electrical and Electronic Engineering
- Applied Mathematics
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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 journal › Article
TY - JOUR
T1 - Iterative convex refinement for sparse recovery
AU - Mousavi, Hojjat S.
AU - Monga, Vishal
AU - Tran, Trac D.
PY - 2015/11/1
Y1 - 2015/11/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84933527510&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84933527510&partnerID=8YFLogxK
U2 - 10.1109/LSP.2015.2438255
DO - 10.1109/LSP.2015.2438255
M3 - Article
AN - SCOPUS:84933527510
VL - 22
SP - 1903
EP - 1907
JO - IEEE Signal Processing Letters
JF - IEEE Signal Processing Letters
SN - 1070-9908
IS - 11
M1 - 7114220
ER -