Restricted isometry property for matrices whose entries are random variables belonging to some Orlicz spaces

Author:
V. B. Troshki

Translated by:
N. Semenov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **91** (2014).

Journal:
Theor. Probability and Math. Statist. **91** (2015), 193-203

MSC (2010):
Primary 68P30; Secondary 68W20

DOI:
https://doi.org/10.1090/tpms/977

Published electronically:
February 4, 2016

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A new approach to the signal processing called compressive sensing has been extensively developed during the last few years. There are many papers devoted to this topic but the problem of constructing the universal measurement matrix has not yet been solved. We propose to use a matrix whose entries are random variables belonging to some Orlicz spaces as a measurement matrix. We prove that the matrix with such entries satisfies the so-called restricted isometry property which is one of the main concepts in compressive sensing.

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Additional Information

**V. B. Troshki**

Affiliation:
Department of Probability Theory and Mathematical Analysis, Faculty of Mathematics, Uzhgorod National University, Universytets’ka Street, 14, Uzhgorod 88000, Ukraine

Email:
btroshki@ukr.net

DOI:
https://doi.org/10.1090/tpms/977

Keywords:
Orlicz space,
restricted isometry property,
compressive sensing

Received by editor(s):
September 9, 2014

Published electronically:
February 4, 2016

Article copyright:
© Copyright 2016
American Mathematical Society