Theory of Probability and Mathematical Statistics
Restricted isometry property for matrices whose entries are random variables belonging to some Orlicz spaces L_U(Ω)
V. B. Troshki
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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(Ω) 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.
Keywords: Orlicz space, restricted isometry property, compressive sensing
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