Toeplitz-Structured Chaotic Sensing Matrix for Compressive Sensing

Lei Yu (1, 2, 3) , Jean-Pierre Barbot (1, 2) , Gang Zheng (1) , Hong Sun (3)

1 ALIEN - Algebra for Digital Identification and Estimation
2 ECS-Lab - Électronique et Commande des Systèmes Laboratoire
3 SPL - Signal Processing Laboratory - Wuhan University

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.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Lei Yu, Jean-Pierre Barbot, Gang Zheng, Hong Sun. Toeplitz-Structured Chaotic Sensing Matrix for Compressive Sensing. IEEE, IET International Symposium on COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING, Oct 2010, Newcastle, United Kingdom. ⟨inria-00530050⟩