Statistical RIP and Semi-Circle Distribution of Incoherent Dictionaries
| dc.creator | Gurevich, Shamgar | |
| dc.creator | Hadani, Ronny | |
| dc.date | 2009-03-20 | |
| dc.date.accessioned | 2026-07-07T12:55:30Z | |
| dc.date.available | 2026-07-07T12:55:30Z | |
| dc.description | 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. | |
| dc.description | This version Includes all the proofs. Submitted for publication (2009) | |
| dc.identifier | https://arxiv.org/abs/0903.3627 | |
| dc.identifier | http://arxiv.org/abs/0903.3627 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224271 | |
| dc.subject | Information Theory | |
| dc.subject | Discrete Mathematics | |
| dc.subject | Probability | |
| dc.title | Statistical RIP and Semi-Circle Distribution of Incoherent Dictionaries | |
| dc.type | text |