标题： 基于相干性的正交匹配追踪性能保证 显示英文标题

标题： Coherence-Based Performance Guarantees of Orthogonal Matching Pursuit

摘要： 在本文中，我们提出了基于一致性的性能保证，用于正交匹配追踪（OMP）在测量受噪声污染时对稀疏信号的支持恢复和信号重建。特别地，分析了两种OMP变体，一种是已知稀疏度的情况，另一种是具有停止规则的情况。结果显示，如果测量矩阵$X\in\mathbb{C}^{n\times p}$满足强一致性性质，则在$n\gtrsim\mathcal{O}(k\log p)$下，OMP将以高概率恢复一个$k$-稀疏信号。特别地，此处获得的性能保证将测量矩阵所需的属性与信号所需的属性分开，这关键取决于最小信噪比，而不是信号的功率分布。我们还提供了部分支持恢复的性能保证。与其他使用最坏情况分析和排序一步阈值算法的OMP性能保证进行了比较。 显示英文摘要

摘要： In this paper, we present coherence-based performance guarantees of Orthogonal Matching Pursuit (OMP) for both support recovery and signal reconstruction of sparse signals when the measurements are corrupted by noise. In particular, two variants of OMP either with known sparsity level or with a stopping rule are analyzed. It is shown that if the measurement matrix $X\in\mathbb{C}^{n\times p}$ satisfies the strong coherence property, then with $n\gtrsim\mathcal{O}(k\log p)$, OMP will recover a $k$-sparse signal with high probability. In particular, the performance guarantees obtained here separate the properties required of the measurement matrix from the properties required of the signal, which depends critically on the minimum signal to noise ratio rather than the power profiles of the signal. We also provide performance guarantees for partial support recovery. Comparisons are given with other performance guarantees for OMP using worst-case analysis and the sorted one step thresholding algorithm.