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

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

2008-12-14

arxiv.org/abs/0812.2602v1

Computer Science

Information Theory

Submitted for The 2009 IEEE International Symposium on Information Theory; Key words: Compressive sensing, Stastical version o

Scientific paper

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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