Improved Bounds for Restricted Isometry Constants
نویسندگان
چکیده
منابع مشابه
Improved Bounds on Restricted Isometry Constants
The restricted isometry constant (RIC) of a matrix A measures how close to an isometry is the action of A on vectors with few nonzero entries, measured in the 2 norm. Specifically, the upper and lower RICs of a matrix A of size n×N are the maximum and the minimum deviation from unity (one) of the largest and smallest, respectively, square of singular values of all (N k ) matrices formed by taki...
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The Restricted Isometry Constants (RIC) of a matrix A measures how close to an isometry is the action of A on vectors with few nonzero entries, measured in the `2 norm. Specifically, the upper and lower RIC of a matrix A of size n ×N is the maximum and the minimum deviation from unity (one) of the largest and smallest, respectively, square of singular values of all `N k ́ matrices formed by taki...
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In this paper we look at isometry properties of random matrices. During the last decade these properties gained a lot attention in a field called compressed sensing in first place due to their initial use in [7, 8]. Namely, in [7, 8] these quantities were used as a critical tool in providing a rigorous analysis of l1 optimization’s ability to solve an under-determined system of linear equations...
متن کاملImproved bounds on Restricted isometry for compressed sensing
This paper discusses new bounds for restricted isometry property in compressed sensing. In the literature, E.J. Candès has proved that δ2s < √ 2 − 1 is a sufficient condition via l1 optimization having s-sparse vector solution. Later, many researchers have improved the sufficient conditions on δ2s or δs. In this paper, we have improved the sufficient condition to δs < 0.309 and have given the s...
متن کاملOn Support Sizes of Restricted Isometry Constants
A generic tool for analyzing sparse approximation algorithms is the restricted isometry property (RIP) introduced by Candès and Tao. For qualitative comparison of sufficient conditions derived from an RIP analysis, the support size of the RIP constants is generally reduced as much as possible with the goal of achieving a support size of twice the sparsity of the target signal. Using a quantitat...
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ژورنال
عنوان ژورنال: Discrete Dynamics in Nature and Society
سال: 2012
ISSN: 1026-0226,1607-887X
DOI: 10.1155/2012/841261