p-RIP CONDITION FOR SIGNAL RECOVERY VIA lp MINIMIZATION

We are concerned with the recovery of both sparse and partially sparse signals via p l minimization. In sparse recovery, the concept of null space property via quasinorm p l ( p-NSP) and the concept of p-restricted isometry property ( p-RIP) for 1 0 < p are very important, while the relation between them has not been studied. First, we will investigate the relation between the p-RIP and the p-NSP. Using the p-RIP, we get a sufficient condition for sparse signal FENGONG WU et al. 22 recovery from noisy measurements. Then, we generalize these properties to the partially sparse recovery and extend the result to partially sparse recovery based on the partially p-RIP.