New bounds for restricted isometry constants

Abstract--This paper discusses new bounds for restricted isometry constants in compressed sensing. Let 8be an n2p real matrix and k be a positive integer with k n. One of the main results of this paper shows that if the restricted isometry constant k of 8 satisfies k < 0:307 then k-sparse signals are guaranteed to be recovered exactly via `1 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 k = k01 2k01 < 0:5, but it is impossible to recover certain k-sparse signals.

• Type: Journal
• Year: 2010
• Where: TIT
• Authors: T. Tony Cai, Lie Wang, Guangwu Xu
• Keywords: Certain K-sparse Signals, Education, K-sparse Signals, Restricted Isometry Constant, TIT 2010