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