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

摘要

In this paper, by generalizing the notion of restricted p-isometry constant (0＜p≤1) defined by Chartrand and Staneva 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.