### 信息科学技术学院建院20周年系列：网络空间安全学院学术讲座(八、九、十、十一)

Orthogonal multi-matching pursuit (OMMP), which is an extension of the OMP algorithm, has better recovery performance than OMP. This paper provides a nearly optimal number of iterations for OMMP.Specifically, we show that if the matrix mathbf{A}\in\mathbb{R}^{m\times n}$satisfies the restricted isometry property (RIP) with$\delta_{6K}\leq0.026$,then OMMP provides a stable reconstruction of$\mathbf{x}$in$\lceil\frac{4K}{M}\rceil$iterations, where$M$is the number of indices chosen in each iteration of the OMMP algorithm.Furthermore, we build an upper bound on the recovery error with fewer required iterations than existing results. These results show that the required number of iterationsto ensure stable recovery of any$K\$-sparse signals are fewer than those required by the start-of-the-art results.

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