Construction of compressive measurement matrix based on convolution of fractional chaos and cyclic matrix

Li-Lian Huang; Min Li; Jian-Hong Xiang

doi:10.1117/1.JEI.27.6.063030

20 December 2018 Construction of compressive measurement matrix based on convolution of fractional chaos and cyclic matrix

Li-Lian Huang, Min Li, Jian-Hong Xiang

Author Affiliations +

Journal of Electronic Imaging, Vol. 27, Issue 6, 063030 (December 2018). https://doi.org/10.1117/1.JEI.27.6.063030

Abstract

A method is proposed to construct an improved measurement matrix—chaotic cyclic convolution measurement matrix (CCCMM). It is constructed by convoluting the fractional order Lorenz chaotic sequences and the cyclic matrix; since cyclic matrix is easy to implement on hardware, accurate reconstructed signal can be obtained by using fractional order chaos with pseudorandomness and convoluting them makes computing results smooth. Meanwhile, CCCMM is proved to have the high probability to satisfy the restricted isometry property. Then, the one-dimensional signals and two-dimensional images are simulated by the CCCMM and other methods, and the results show that the CCCMM is more superior in evaluating recovered signals with parameters and the visual effect of the restored images.

Citation Download Citation

Li-Lian Huang, Min Li, and Jian-Hong Xiang "Construction of compressive measurement matrix based on convolution of fractional chaos and cyclic matrix," Journal of Electronic Imaging 27(6), 063030 (20 December 2018). https://doi.org/10.1117/1.JEI.27.6.063030

Received: 8 May 2018; Accepted: 29 November 2018; Published: 20 December 2018

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