Statistics Papers
Document Type
Journal Article
Date of this Version
9-2010
Publication Source
IEEE Transactions on Information Theory
Volume
56
Issue
9
Start Page
4388
Last Page
4394
DOI
10.1109/TIT.2010.2054730
Abstract
This paper discusses new bounds for restricted isometry constants in compressed sensing. Let Φ be an n × p real matrix and A; be a positive integer with k ≤ n. One of the main results of this paper shows that if the restricted isometry constant δk of Φ satisfies δk <; 0.307 then k-sparse signals are guaranteed to be recovered exactly via ℓ1 minimization when no noise is present and k-sparse signals can be estimated stably in the noisy case. It is also shown that the bound cannot be substantially improved. An explicit example is constructed in which δk = k-1/2k-1 <; 0.5, but it is impossible to recover certain k-sparse signals.
Keywords
minimisation, sparse matrices, compressed sensing, k-sparse signal, minimization, positive integer, real matrix, restricted isometry constant, computer aided instruction, linear matrix inequalities, mathematics, measurement errors, minimization methods, noise, noise measurement, signal processing, statistics, upper bound, vectors, restricted isometry property, sparse signal recovery
Recommended Citation
Cai, T., Wang, L., & Xu, G. (2010). New Bounds for Restricted Isometry Constants. IEEE Transactions on Information Theory, 56 (9), 4388-4394. http://dx.doi.org/10.1109/TIT.2010.2054730
Included in
Applied Mathematics Commons, Computer Sciences Commons, Statistics and Probability Commons
Date Posted: 27 November 2017
This document has been peer reviewed.