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Correlation-aware sparse support recovery: Gaussian sources

Pal, Piya and Vaidyanathan, P. P. (2013) Correlation-aware sparse support recovery: Gaussian sources. In: 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing. IEEE , Piscataway, NJ, pp. 5880-5884. ISBN 978-1-4799-0356-6. https://resolver.caltech.edu/CaltechAUTHORS:20140225-110454867

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Abstract

Consider a multiple measurement vector (MMV) model given by y[n] = Ax_s[n]; 1 ≤ n ≤ L where {y[n]}^L_n=1 denote the L measurement vectors, A ∈ R^(M×N) is the measurement matrix and x_s[n] ∈ R^N are the unknown vectors with same sparsity support denoted by the set S_0 with |S_0| = D. It has been shown in a recent paper by the authors that when the elements of x_s[n] are uncorrelated from each other, one can recover sparsity levels as high as O(M^2) for suitably designed measurement matrix. The recovery is exact when support recovery algorithms are applied on the ideal correlation matrix. When we only have estimates of the correlation, it is still possible to probabilistically argue the recovery of sparsity levels (using a coherence based argument) that is much higher than that guaranteed by existing coherence based results. However the lower bound on the probability of success is found to increase rather slowly with L (as 1-C/L for some constant C > 0) without any further assumption on the distribution of the source vectors. In this paper, we demonstrate that when the source vectors belong to a Gaussian distribution with diagonal covariance matrix, it is possible to guarantee the recovery of original support with overwhelming probability. We also provide numerical simulations to demonstrate the effectiveness of the proposed strategy by comparing it with other popular MMV based methods.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ICASSP.2013.6638792DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6638792PublisherArticle
ORCID:
AuthorORCID
Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© 2013 IEEE. Date of Conference: 26-31 May 2013. Work supported in parts by the ONR grant N00014-11-1-0676, and the California Institute of Technology.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-11-1-0676
CaltechUNSPECIFIED
Subject Keywords:Support Recovery, LASSO, Block Spar- sity, Multiple Measurement Vector (MMV), Correlation.
DOI:10.1109/ICASSP.2013.6638792
Record Number:CaltechAUTHORS:20140225-110454867
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140225-110454867
Official Citation:Pal, P.; Vaidyanathan, P.P., "Correlation-aware sparse support recovery: Gaussian sources," Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on , vol., no., pp.5880,5884, 26-31 May 2013 doi: 10.1109/ICASSP.2013.6638792
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:43980
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:25 Feb 2014 20:56
Last Modified:10 Nov 2021 16:46

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