RIP Analysis for $\ell _{1}/\ell _{p}$ ($p> 1$) Minimization Method

Recently, non-convex and non-linear metrics have been introduced in compressed sensing to promote sparsity. This letter proposes an extension of the previously proposed $\ell _{1}/\ell _{2}$ minimization method for sparse recovery using the $\ell _{1}/\ell _{p}$ minimization method with $p\gt 1$ . We establish sufficient conditions for the $\ell _{1}/\ell _{p}$ minimization to recover sparse signals under the restricted isometry property (RIP). Additionally, we develop an effective algorithm to solve the $\ell _{1}/\ell _{p}$ minimization problem. Experiments show the proposed method is comparable to state-of-the-art methods for sparse signal recovery.