Statistical RIP and Semi-Circle Distribution of Incoherent Dictionaries
Abstract
In this paper we formulate and prove 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 prove 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.
Keywords
Cite
@article{arxiv.0903.3627,
title = {Statistical RIP and Semi-Circle Distribution of Incoherent Dictionaries},
author = {Shamgar Gurevich and Ronny Hadani},
journal= {arXiv preprint arXiv:0903.3627},
year = {2009}
}
Comments
This version Includes all the proofs. Submitted for publication (2009)