Restricted p-isometry properties of nonconvex block-sparse compressed sensing

In this paper, by generalizing the notion of restricted p-isometry constant (0 < p <= 1) defined by Chartrand and Staneva [1] to the setting of block-sparse signal recovery, we establish a general restricted p-isometry property (p-RIP) condition for recovery of (nearly) block-sparse signals via mixed l(2)/l(p)-minimization. Moreover, we derive a lower bound on the necessary number of Gaussian measurements for the p-RIP condition to hold with high probability, which shows clearly that fewer measurements with smaller p are needed for exact recovery of block-sparse signals via mixed l(2)/l(p)-minimization than when p=1. (C) 2014 Elsevier B.V. All rights reserved.