Limits of Deterministic Compressed Sensing Considering Arbitrary Orthonormal Basis for Sparsity

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dc.creatorAmini, Arash
dc.creatorMarvasti, Farokh
dc.date2009-01-22
dc.date.accessioned2026-07-07T12:32:55Z
dc.date.available2026-07-07T12:32:55Z
dc.descriptionIt is previously shown that proper random linear samples of a finite discrete signal (vector) which has a sparse representation in an orthonormal basis make it possible (with probability 1) to recover the original signal. Moreover, the choice of the linear samples does not depend on the sparsity domain. In this paper, we will show that the replacement of random linear samples with deterministic functions of the signal (not necessarily linear) will not result in unique reconstruction of k-sparse signals except for k=1. We will show that there exist deterministic nonlinear sampling functions for unique reconstruction of 1- sparse signals while deterministic linear samples fail to do so.
dc.description4 pages, submitted to SAMPTA2009
dc.identifierhttps://arxiv.org/abs/0901.3408
dc.identifierhttp://arxiv.org/abs/0901.3408
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216948
dc.subjectInformation Theory
dc.titleLimits of Deterministic Compressed Sensing Considering Arbitrary Orthonormal Basis for Sparsity
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