The Improved Bounds of Restricted Isometry Constant for Recovery via $\ell_{p}$ -Minimization

Nonconvex l p -minimization with p ∈ (0,1) has been studied recently in the context of compressed sensing. In this paper, we prove that as long as the sensing matrix A ∈ R m×n satisfies restricted isometry property with δ 2k ∈ (0,1), every k-sparse signal x ∈ R n can be recovered exactly from linear measurement y=Ax via solving some l p -minimization problem. In fact, it is shown that p 2k )} suffices for the exact k-sparse recovery of l p -minimization, which improves the existing results greatly.