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arXiv 0812.26022008-12-14cs.ITcs.DMmath.ITmath.PR

非相干字典的统计限制等距性和Wigner周期分布

The statistical restricted isometry property and the Wigner semicircle distribution of incoherent dictionaries

Shamgar Gurevich, Ronny Hadani

备注：: Submitted for The 2009 IEEE International Symposium on Information Theory; Key words: Compressive sensing, Stastical version of Candes-Tao RIP, Incoherent Dictionaries, Semicircle distribution

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摘要：

在这篇文章中，我们提出了一个统计版本的Candes-Tao限制等距属性（简称SRIP），它一般适用于任何不相干的字典，这是一个不相交的标准正交基的联合。此外，我们表明，在适当的规范化，相关的革兰氏矩阵的特征值波动在1左右，根据Wigner周期分布。然后将结果应用到各种字典中自然出现的有限谐波分析的设置，给，特别是一个更好的理解上的一句话的Applebaum霍华德Searle-Calderbank关于RIP的海森堡字典啁啾一样的功能。

英文摘要：

In this article we present a statistical version of the Candes-Tao restricted isometry property (SRIP for short) which holds in general for any incoherent dictionary which is a disjoint union of orthonormal bases. In addition, we show that, under appropriate normalization, the eigenvalues of the associated Gram matrix fluctuate around 1 according to the Wigner semicircle distribution. The result is then applied to various dictionaries that arise naturally in the setting of finite harmonic analysis, giving, in particular, a better understanding on a remark of Applebaum-Howard-Searle-Calderbank concerning RIP for the Heisenberg dictionary of chirp like functions.

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