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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board Member: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre

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CiteScore 2016: 0.37

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Source Normalized Impact per Paper (SNIP) 2016: 0.793

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1569-397X
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Volume 23, Issue 3 (Sep 2015)

Issues

The restricted isometry property for random matrices with ϕ-subgaussian entries

Yuriy Kozachenko
  • Department of Probability Theory, Statistics and Actuarial Mathematics, Kyiv National Taras Shevchenko University, 64, Volodymyrs'ka St., 01601 Kyiv, Ukraine
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/ Viktor Troshki
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  • Department of Probability Theory, Statistics and Actuarial Mathematics, Kyiv National Taras Shevchenko University, 64, Volodymyrs'ka St., 01601 Kyiv, Ukraine
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Published Online: 2015-08-13 | DOI: https://doi.org/10.1515/rose-2014-0037

Abstract

The aim of this article is to construct the generalized random matrices, which satisfies the restricted isometry property (as introduced by Candes and Tao). Let the data be presented as a product of a vector with not more than K nonzero coordinates by a given matrix. We show that for such data we can change the upper bound of the variable K. In particular, we prove that the random matrices whose entries are independent realizations of random variables from ϕ-subgaussian space could be used in the theory of compressive sensing for encoding vectors.

Keywords: Compressive sensing; restricted isometry property; ϕ-subgaussian space

MSC: 60F10; 60B20; 94A12

About the article

Received: 2014-10-18

Accepted: 2015-02-20

Published Online: 2015-08-13

Published in Print: 2015-09-01


Citation Information: Random Operators and Stochastic Equations, ISSN (Online) 1569-397X, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/rose-2014-0037.

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