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The sampling rate-distortion tradeoff for sparsity pattern recovery in compressed sensing

Publication ,  Journal Article
Reeves, G; Gastpar, M
Published in: IEEE Transactions on Information Theory
May 1, 2012

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. © 2011 IEEE.

Duke Scholars

Published In

IEEE Transactions on Information Theory

DOI

ISSN

0018-9448

Publication Date

May 1, 2012

Volume

58

Issue

5

Start / End Page

3065 / 3092

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing
 

Citation

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Reeves, G., & Gastpar, M. (2012). The sampling rate-distortion tradeoff for sparsity pattern recovery in compressed sensing. IEEE Transactions on Information Theory, 58(5), 3065–3092. https://doi.org/10.1109/TIT.2012.2184848
Reeves, G., and M. Gastpar. “The sampling rate-distortion tradeoff for sparsity pattern recovery in compressed sensing.” IEEE Transactions on Information Theory 58, no. 5 (May 1, 2012): 3065–92. https://doi.org/10.1109/TIT.2012.2184848.
Reeves G, Gastpar M. The sampling rate-distortion tradeoff for sparsity pattern recovery in compressed sensing. IEEE Transactions on Information Theory. 2012 May 1;58(5):3065–92.
Reeves, G., and M. Gastpar. “The sampling rate-distortion tradeoff for sparsity pattern recovery in compressed sensing.” IEEE Transactions on Information Theory, vol. 58, no. 5, May 2012, pp. 3065–92. Scopus, doi:10.1109/TIT.2012.2184848.
Reeves G, Gastpar M. The sampling rate-distortion tradeoff for sparsity pattern recovery in compressed sensing. IEEE Transactions on Information Theory. 2012 May 1;58(5):3065–3092.

Published In

IEEE Transactions on Information Theory

DOI

ISSN

0018-9448

Publication Date

May 1, 2012

Volume

58

Issue

5

Start / End Page

3065 / 3092

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing