Stable Recovery of Sparse Signals With Non-Convex Weighted $r$-Norm Minus 1-Norm

Abstract

. Given the measurement matrix A and the observation signal y , the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system y = Ax + z , where x is the s -sparse signal to be recovered and z is the noise vector. Zhou and Yu [1] recently proposed a novel non-convex weighted ℓ r − ℓ 1 minimization method for effective sparse recovery. In this paper, we reveal that based on ( y, A ), any s -sparse signal can be robustly reconstructed via this method provided that the mutual coherence µ of A fulfills µ < 1 / ( s − 1 + 2 1 =r − 1 s 1 =r ). To our best of knowledge, this is the first mutual coherence based sufficient condition for such approach.