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Restricted isometry property for matrices whose entries are random variables belonging to some Orlicz spaces $ L_U(\Omega)$


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
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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 $ L_U(\Omega )$ 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

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