# Sparse Support Recovery via Covariance Estimation

Abstract:

We consider the problem of recovering the common support of a set of
$k$-sparse signals $\{\mathbf{x}_{i}\}_{i=1}^{L}$ from noisy linear
underdetermined measurements of the form
$\{{\Phi} \mathbf{x}_{i}+\mathbf{w}_{i}\}_{i=1}^{L}$ where
${\Phi}\in\rr^{m\times N}$ $(m<N)$ is the sensing matrix and
$\mathbf{w}_{i}$ is the additive noise. We employ a Bayesian setup where we impose a Gaussian prior with zero mean and a
common diagonal covariance matrix $\mathbf{\Gamma}$ across all
$\mathbf{x}_{i},$ and formulate the support recovery problem as one of
covariance estimation.
We develop an algorithm to find the
approximate maximum-likelihood estimate of $\mathbf{\Gamma}$ using a
modified reweighted minimization procedure. Empirically, we
find that the proposed algorithm succeeds in exactly recovering
the common support with high probability in the $k<m$ regime with $L$
of the order of $m$ and in the $k\ge m$ regime with larger $L$. The key advantage of the proposed algorithm is that its complexity is independent of $L$, unlike existing sparse support recovery algorithms.

### Paper Details

Authors:
Lekshmi Ramesh, Chandra R. Murthy
Submitted On:
13 April 2018 - 4:06am
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Chandra R. Murthy
Paper Code:
SS-L3.6
Document Year:
2018

### Subscribe

[1] Lekshmi Ramesh, Chandra R. Murthy, "Sparse Support Recovery via Covariance Estimation", IEEE SigPort, 2018. [Online]. Available: http://sigport.org/2646. Accessed: Mar. 25, 2019.
@article{2646-18,
url = {http://sigport.org/2646},
author = {Lekshmi Ramesh; Chandra R. Murthy },
publisher = {IEEE SigPort},
title = {Sparse Support Recovery via Covariance Estimation},
year = {2018} }
TY - EJOUR
T1 - Sparse Support Recovery via Covariance Estimation
AU - Lekshmi Ramesh; Chandra R. Murthy
PY - 2018
PB - IEEE SigPort
UR - http://sigport.org/2646
ER -
Lekshmi Ramesh, Chandra R. Murthy. (2018). Sparse Support Recovery via Covariance Estimation. IEEE SigPort. http://sigport.org/2646
Lekshmi Ramesh, Chandra R. Murthy, 2018. Sparse Support Recovery via Covariance Estimation. Available at: http://sigport.org/2646.
Lekshmi Ramesh, Chandra R. Murthy. (2018). "Sparse Support Recovery via Covariance Estimation." Web.
1. Lekshmi Ramesh, Chandra R. Murthy. Sparse Support Recovery via Covariance Estimation [Internet]. IEEE SigPort; 2018. Available from : http://sigport.org/2646