Compressive Sensing with Chaotic Sequence

International audienceCompressive 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

Toeplitz-Structured Chaotic Sensing Matrix for Compressive Sensing

International audienceCompressive 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

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin