基于相干性理论的非凸块稀疏压缩感知

A coherence theory of nonconvex block-sparse compressed sensing

限制等容性质(restricted isometry property,RIP)在压缩感知的理论研究中占据重要地位.然而,限制等容条件的验证却是一个复杂的组合优化问题.为了克服这一问题,本文将相干性理论引入非凸块稀疏压缩感知理论的研究,得到了块结构信号恢复的两类充分条件.所获结果将基于传统稀疏凸优化问题的相干性理论研究推广至了非凸块稀疏的情形.通过构造一类块相干系数较小的测量矩阵,非凸块稀疏压缩感知策略的有效性得到了数值实验的进一步验证.

The restricted isometry property plays an important role in the theoretical study of compressed sensing.However,the verification of any given restricted isometry conditions is a complex combinatorial optimization problem.To remedy this issue,in this article,we propose a coherence theory of nonconvex block-sparse compressed sensing and obtain two types of sufficient conditions for block-structured signal recovery.The obtained results extend the coherence theory used in the traditional convex sparse recovery case to the nonconvex blocksparse recovery case.With constructing a sort of measurement matrices whose block coherence were proved to be very small,we demonstrate the effectiveness of the strategy for nonconvex block-sparse compressed sensing via a series of simulation studies.