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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.

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