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

Shamgar Gurevich; Ronny Hadani

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arXiv · 0812.2602

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

Shamgar Gurevich·Ronny Hadani

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Abstract

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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Shamgar Gurevich, Ronny Hadani. 2008-12-14. The statistical restricted isometry property and the Wigner semicircle distribution of incoherent dictionaries. https://arxiv.org/abs/0812.2602

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