Sparse Signal Recovery by ℓq Minimization Under Restricted Isometry Property.

In the context of compressed sensing, the nonconvex ℓ_q minimization with 0 < q < 1 has been studied in recent years. In this letter, by generalizing the sharp bound for ℓ₁ minimization of Cai and Zhang, we show that the condition δ(s^q+1)k < 1/√(s^q-2+1) in terms of restricted isometry constant (RIC) can guarantee the exact recovery of k-sparse signals in the noiseless case and the stable recovery of approximately k-sparse signals in the noisy case by ℓ_q minimization. This result is more general than the sharp bound for ℓ₁ minimization when the order of RIC is greater than 2k and illustrates the fact that a better approximation to ℓ₀ minimization is provided by ℓ_q minimization than that provided by ℓ₁ minimization. [ABSTRACT FROM PUBLISHER]