Toeplitz-Structured Chaotic Sensing Matrix for Compressive SensingReport as inadecuate

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1 ALIEN - Algebra for Digital Identification and Estimation Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR8146 2 ECS-Lab - Électronique et Commande des Systèmes Laboratoire 3 SPL - Signal Processing Laboratory - Wuhan University

Abstract : Compressive Sensing CS is a new sampling theory which allows signals to be sampled at sub-Nyquist rate without loss of information. Fundamentally, its procedure can be modeled as a linear projection on one specific sensing matrix, which, in order to guarantee the information conservation, satisfies Restricted Isometry Property RIP. Ordinarily, this matrix is constructed by the Gaussian random matrix or Bernoulli random matrix. In previous work, we have proved that the typical chaotic sequence - logistic map can be adopted to generate the sensing matrix for CS. In this paper, we show that Toeplitz-structured matrix constructed by chaotic sequence is sufficient to satisfy RIP with high probability. With the Toeplitz-structured Chaotic Sensing Matrix TsCSM, we can easily build a filter with small number of taps. Meanwhile, we implement the TsCSM in compressive sensing of images.

Author: Lei Yu - Jean-Pierre Barbot - Gang Zheng - Hong Sun -



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