General RIP bounds of δtk for sparse signals recovery by ℓp minimization

Abstract

In this paper, we establish new restricted isometry conditions for sparse signal recovery via ℓp (0 < p ≤ 1) minimization. For any t ∈ (1, 2], the restricted isometry constant (RIC) condition δtkA<f(t,p), where f(t, p) increases monotonically with respect to t, can guarantee the exact recovery of all k-sparse signals in the noiseless case and the stable recovery of approximately k-sparse signals in noisy cases via the constrained ℓp minimization. The obtained results extend the recent ones in [2], which deals with δ2kA and therein the original signal is required to be k-sparse in the noisy cases.