NDLI: On application of LASSO for sparse support recovery with imperfect correlation awareness

Content Provider	IEEE Xplore Digital Library
Author	Pal, P. Vaidyanathan, P.P.
Copyright Year	2012
Description	Author affiliation: Dept. of Electrical Engineering, MC 136-93, California Institute of Technology, Pasadena, 91125, USA (Pal, P.; Vaidyanathan, P.P.)
Abstract	In this paper, the problem of identifying the common sparsity support of multiple measurement vectors (MMV) is considered. The model is given by y[n] = Ax[n], 1 ⋄ n ⋄ L where ${y[n]}^{L}$ denote the L measurement vectors, A ∈ $R^{M×N}$ is the measurement matrix and x[n] ∈ $R^{N}$ are the unknown vectors with same sparsity support denoted by the set S with \|S\| = D. It has been shown in a recent paper by the authors that when the elements of x[n] are uncorrelated from each other, one can recover sparsity levels as high as $O(M^{2})$ for suitably designed measurement matrix. This result was shown assuming the knowledge that the nonzero elements are perfectly uncorrelated and that we have perfect estimates for the data correlation matrix, (the latter is true in the limit as L → ∞). In this paper, we formulate the problem of support recovery in the non ideal setting, i.e., when the correlation matrix is estimated with finite L. The resulting support recovery problem which explicitly utilizes the correlation knowledge, can be formulated as a LASSO. The performance of such “correlation aware” LASSO is analyzed by providing lower bounds on the probability of successful recovery as a function of the number L of measurement vectors. Numerical results are also provided to demonstrate the superior performance of the proposed correlation aware framework over conventional MMV techniques under identical conditions.
Starting Page	958
Ending Page	962
File Size	1017976
Page Count	5
File Format	PDF
ISBN	9781467350501
ISSN	10586393
e-ISBN	9781467350518
DOI	10.1109/ACSSC.2012.6489158
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-11-04
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Correlation Support Recovery LASSO Block Sparsity Multiple Measurement Vector (MMV)
Content Type	Text
Resource Type	Article
Subject	Signal Processing Computer Networks and Communications

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