New Bounds for Restricted Isometry Constants

• Main Authors: Cai, T. Tony (Author), Wang, Lie (Contributor), Xu, Guangwu (Author)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Institute of Electrical and Electronics Engineers, 2011-10-19T17:38:42Z.
• Subjects: Article
• Online Access: Get fulltext

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.
National Science Foundation (U.S.). Focused Research Group (Grant DMS-0854973)
National Basic Research Program of China (973 Program) (No. 2007CB807902)