New Bounds for RIC in Compressed Sensing

Abstract

This paper gives new bounds for restricted isometry constant (RIC) in compressed sensing. Let Φ be an m×n real matrix and k be a positive integer with k≤n. The main results of this paper show that if the restricted isometry constant of Φ satisfies δ8ak<1 and (Formula presented.) for a> 3/8, then k-sparse solution can be recovered exactly via l1 minimization in the noiseless case. In particular, when a=1,1.5,2 and 3, we have δ2k<0.5746 and δ8k<1, or δ2.5k<0.7046 and δ12k<1, or δ3k<0.7731 and δ16k<1 or δ4k<0.8445 and δ24k<1. © 2013 The Author(s).