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

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Reeves, G; Gastpar, M

Published Date

  • May 1, 2012

Published In

Volume / Issue

  • 58 / 5

Start / End Page

  • 3065 - 3092

International Standard Serial Number (ISSN)

  • 0018-9448

Digital Object Identifier (DOI)

  • 10.1109/TIT.2012.2184848

Citation Source

  • Scopus