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:
- 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
- Cite

### Keywords

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url = {http://sigport.org/2646},

author = {Lekshmi Ramesh; Chandra R. Murthy },

publisher = {IEEE SigPort},

title = {Sparse Support Recovery via Covariance Estimation},

year = {2018} }

T1 - Sparse Support Recovery via Covariance Estimation

AU - Lekshmi Ramesh; Chandra R. Murthy

PY - 2018

PB - IEEE SigPort

UR - http://sigport.org/2646

ER -