Uniform RIP Bounds for Recovery of Signals with Partial Support Information by Weighted ℓ_p-Minimization

In this paper, we consider signal recovery in both noiseless and noisy cases via weighted ℓ_p (0 < p≤ 1) minimization when some partial support information on the signals is available. The uniform sufficient condition based on restricted isometry property (RIP) of order tk for any given constant t>d (d≥1 is determined by the prior support information) guarantees the recovery of all k-sparse signals with partial support information. The new uniform RIP conditions extend the state-of-the-art results for weighted ℓ_p-minimization in the literature to a complete regime, which fill the gap for any given constant t> 2d on the RIP parameter, and include the existing optimal conditions for the ℓ_p-minimization and the weighted ℓ₁-minimization as special cases.