A Sufficient Condition of Non-Convex ${\ell }_{p} -\beta {\ell }_{q}$ Minimization for Sparse Recovery

To recover sparse signals via ${\ell }_{p}-\beta {\ell }_{q}$ minimization with parameters $0 < p \leq 1$, $1 \leq q \leq 2$ ($p\ne q$) and $0 \leq \beta \leq 1$, this letter employs the Restricted Isometry Property (RIP) and Restricted Orthogonality Property (ROP) to investigate sparse signal recovery in the noise setting. Based on these analyses, a sufficient condition is proposed, which generalizes and improves state-of-the-art results. In Section III, several key remarks are presented. Our results also demonstrate that the derived condition outperforms the existing ones.