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Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise

机译:正交匹配追踪,用于噪声少的信号恢复

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摘要

We consider the orthogonal matching pursuit (OMP) algorithm for the recovery of a high-dimensional sparse signal based on a small number of noisy linear measurements. OMP is an iterative greedy algorithm that selects at each step the column, which is most correlated with the current residuals. In this paper, we present a fully data driven OMP algorithm with explicit stopping rules. It is shown that under conditions on the mutual incoherence and the minimum magnitude of the nonzero components of the signal, the support of the signal can be recovered exactly by the OMP algorithm with high probability. In addition, we also consider the problem of identifying significant components in the case where some of the nonzero components are possibly small. It is shown that in this case the OMP algorithm will still select all the significant components before possibly selecting incorrect ones. Moreover, with modified stopping rules, the OMP algorithm can ensure that no zero components are selected.
机译:我们考虑基于少量噪声线性测量的正交匹配追踪(OMP)算法来恢复高维稀疏信号。 OMP是一种迭代贪婪算法,它在每个步骤中选择与当前残差最相关的列。在本文中,我们提出了具有明确停止规则的完全数据驱动的OMP算法。结果表明,在互不相干和信号非零分量最小幅度的条件下,利用OMP算法可以高概率准确地恢复信号的支持。另外,在某些非零分量可能很小的情况下,我们还考虑了识别重要分量的问题。结果表明,在这种情况下,OMP算法仍将选择所有重要组件,然后再选择不正确的组件。此外,通过修改的停止规则,OMP算法可以确保没有选择零分量。

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