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

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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.
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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Information Theory, Discrete Mathematics, Probability

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http://salesiana.dossiersoluciones.com/handle/123456789/210647

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0812.2602
 http://arxiv.org/abs/0812.2602

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arXiv