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Compressive Sensing with Chaotic Sequence

Lei yu 1, 2, 3 Jean-Pierre Barbot 1, 2 Gang Zheng 1 Hong Sun 3 
1 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Centrale Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
Abstract : Compressive sensing is a new methodology to cap- ture signals at sub-Nyquist rate. To guarantee exact recovery from compressed measurements, one should choose specific matrix, which satisfies the Restricted Isometry Property (RIP), to implement the sensing procedure. In this letter, we propose to construct the sensing matrix with chaotic sequence following a trivial method and prove that with overwhelming probability, the RIP of this kind of matrix is guaranteed. Meanwhile, its experimental comparisons with Gaussian random matrix, Bernoulli random matrix and sparse matrix are carried out and show that the performances among these sensing matrix are almost equal.
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Lei yu, Jean-Pierre Barbot, Gang Zheng, Hong Sun. Compressive Sensing with Chaotic Sequence. IEEE Signal Processing Letters, Institute of Electrical and Electronics Engineers, 2010, 17 (8), pp.731 - 734. ⟨10.1109/LSP.2010.2052243⟩. ⟨inria-00530058⟩

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