Approximate sparsity pattern recovery: Information-theoretic lower bounds

Journal Article (Journal Article)

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown that if the measurement rate and per-sample signal-to-noise ratio (SNR) are finite constants independent of the length of the vector, then the optimal sparsity pattern estimate will have a constant fraction of errors. Lower 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. 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 achievable bounds. Near optimality is shown for a wide variety of practically motivated signal models. © 1963-2012 IEEE.

Full Text

Duke Authors

Cited Authors

  • Reeves, G; Gastpar, MC

Published Date

  • May 23, 2013

Published In

Volume / Issue

  • 59 / 6

Start / End Page

  • 3451 - 3465

International Standard Serial Number (ISSN)

  • 0018-9448

Digital Object Identifier (DOI)

  • 10.1109/TIT.2013.2253852

Citation Source

  • Scopus