Restricted p isometry properties of nonconvex block sparse compressed sensing
Abstract 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 l2/lp 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 l2/lp minimization than when p=1.
Signal Process.