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首页> 外文期刊>Information Theory, IEEE Transactions on >Joint src='/images/tex/348.gif' alt='k'> -Step Analysis of Orthogonal Matching Pursuit and Orthogonal Least Squares
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Joint src='/images/tex/348.gif' alt='k'> -Step Analysis of Orthogonal Matching Pursuit and Orthogonal Least Squares

机译：联合 src =“ / images / tex / 348.gif” alt =“ k”> -正交匹配追踪和正交最小二乘法的步骤分析

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摘要

Tropp's analysis of orthogonal matching pursuit (OMP) using the exact recovery condition (ERC) is extended to a first exact recovery analysis of orthogonal least squares (OLS). We show that when the ERC is met, OLS is guaranteed to exactly recover the unknown support in at most $k$ iterations where $k$ denotes the support cardinality. Moreover, we provide a closer look at the analysis of both OMP and OLS when the ERC is not fulfilled. The existence of dictionaries for which some subsets are never recovered by OMP is proved. This phenomenon also appears with basis pursuit where support recovery depends on the sign patterns, but it does not occur for OLS. Finally, numerical experiments show that none of the considered algorithms is uniformly better than the other but for correlated dictionaries, guaranteed exact recovery may be obtained after fewer iterations for OLS than for OMP.
机译：使用精确恢复条件（ERC）对正交匹配追踪（OMP）的Tropp分析扩展到正交最小二乘（OLS）的第一个精确恢复分析。我们证明，当满足ERC要求时，OLS可以保证最多在 $ k $ 迭代中准确地恢复未知支持。 $ k $ 表示支持基数。此外，当ERC不满足时，我们将更仔细地分析OMP和OLS。证明了存在某些OMP无法恢复某些子集的字典。在支持恢复取决于符号模式的基础追求中，也会出现此现象，但对于OLS不会发生。最终，数值实验表明，所考虑的算法均不能比其他算法更好，但是对于相关字典，OLS的迭代次数要比OMP少，因此可以保证准确的恢复。

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