New RIP Bounds for Recovery of Sparse Signals With Partial Support Information via Weighted lp-Minimization

In this paper, we consider the recovery of k-sparse signals using the weighted l(p) (0 < p <= 1) minimization when some partial prior information on the support is available. First, we present a unified analysis of restricted isometry constant delta(tk) with d < t <= 2d (d >= 1 is determined by the prior support information) for sparse signal recovery by the weighted l(p) (0 < p <= 1) minimization in both noiseless and noisy settings. This result fills a vacancy on delta(tk) with t < 2, compared with previous works on delta((a+1))k (a > 1). Second, we provide a sufficient condition on delta(tk) with 1 < t <= 2 for the recovery of sparse signals using the l(p) (0 < p <= 1) minimization, which extends the existing optimal result on delta(2k) in the literature. Last, various numerical examples are presented to demonstrate the better performance of the weighted l(p) (0 < p <= 1) minimization is achieved when the accuracy of prior information on the support is at least 50%, compared with that of the l(p) (0 < p <= 1) minimization.