The sampling rate-distortion tradeoff for sparsity pattern recovery in compressed sensing
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
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Networking & Telecommunications
- 1005 Communications Technologies
- 0906 Electrical and Electronic Engineering
- 0801 Artificial Intelligence and Image Processing
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Networking & Telecommunications
- 1005 Communications Technologies
- 0906 Electrical and Electronic Engineering
- 0801 Artificial Intelligence and Image Processing