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

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Date Posted: 27 November 2017

This document has been peer reviewed.