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research article

The Sampling Rate-Distortion Tradeoff for Sparsity Pattern Recovery in Compressed Sensing

Reeves, Galen Andrew  
•
Gastpar, Michael C.  
2012
IEEE Transactions on Information Theory

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a vanishing fraction of errors is impossible if the measurement rate and the per-sample signal-to-noise ratio (SNR) are finite constants, independent of the vector length. In this paper, it is shown that recovery with an arbitrarily small but constant fraction of errors is, however, possible, and that in some cases computationally simple estimators are near-optimal. Bounds on the measurement rate needed to attain a desired fraction of errors are given in terms of the SNR and various key parameters of the unknown vector for several different recovery algorithms. The tightness of the bounds, in a scaling sense, as a function of the SNR and the fraction of errors, is established by comparison with existing information-theoretic necessary bounds. Near optimality is shown for a wide variety of practically motivated signal models.

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Type
research article
DOI
10.1109/TIT.2012.2184848
Web of Science ID

WOS:000303204900034

Author(s)
Reeves, Galen Andrew  
Gastpar, Michael C.  
Date Issued

2012

Publisher

Institute of Electrical and Electronics Engineers

Published in
IEEE Transactions on Information Theory
Volume

58

Issue

5

Start page

3065

End page

3092

Subjects

Compressed sensing

•

message passing algorithms

•

model selection

•

random matrix theory

•

sparsity

•

support recovery

URL

URL

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6142088&contentType=Journals+%26+Magazines&sortType%3Dasc_p_Sequence%26filter%3DAND%28p_IS_Number%3A6185725%29%26pageNumber%3D2
Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
LINX  
Available on Infoscience
May 9, 2012
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/80179
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