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Construction of a Class of Logistic Chaotic Measurement Matrices for Compressed Sensing

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Abstract

The construction of the measurement matrix is the key technology for accurate recovery of compressed sensing. In this paper, we demonstrated correlation properties of nonpiecewise and piecewise logistic chaos system to follow Gaussian distribution. The correlation properties can generate a class of logistic chaotic measurement matrices with simple structure, easy hardware implementation and ideal measurement efficiency. Specifically, spread spectrum sequences generated by the correlation properties follow Gaussian distribution. Thus, the proposed algorithm constructs chaos-Gaussian matrices by the sequences. Simulation results of one-dimensional signals and two-dimensional images show that chaos-Gaussian measurement matrices can provide comparable performance against common random measurement matrices. In addition, chaos-Gaussian matrices are deterministic measurement matrices.

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Funding

This work is supported by the North East Petroleum University Natural Science Foundation under Grant nos. 2017PYZL-05, JYCX_CX06_2018, and JYCX_JG06_2018.

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Authors and Affiliations

  1. School of Electrical and Information Engineering, Northeast Petroleum University, Daqing, China

    Xiaoxue Kong, Hongbo Bi, Di Lu & Ning Li

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  1. Xiaoxue Kong
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  2. Hongbo Bi
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  3. Di Lu
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  4. Ning Li
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Corresponding author

Correspondence to Hongbo Bi.

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The authors declare that they have no conflicts of interest.

Additional information

Xiaoxue Kong, born in 1993, received her bachelor degree from the Hebei Normal University of Science and Technology, China, in 2017. Currently, she is a graduate student in North East Petroleum University, China. Her research interests comprise compressive sensing, object recognition and detection, etc.

Hongbo Bi, born in 1979, received his bachelor degree and master degree in communications engineering from North East Petroleum University, China, in 2001 and 2004, respectively. He received his PhD in 2013 from Beijing University of Posts and Telecommunications and worked as a PDF (PostDoc Fellow) in Harbin Engineering University in 2014–2017. He is also worked as a visiting scholar in University of Waterloo (Canada) in 2014–2015. Currently, he is an associate professor in School of Electrical Information Engineering in North East Petroleum University. Hismain research interests focus on saliency detection, compressive sensing, deep learning, digital watermarking, signal processing, etc.

Di Lu, born in 1993, received his bachelor degree from the North East Petroleum University, China, in 2016. Currently, he is a graduate student in North East Petroleum University, China. His research interests vidio saliency detection tasks, etc.

Ning Li, born in 1990, received his bachelor degree from Huanghuai University, China, in 2015. Currently, he is a graduate student in North East Petroleum University, China. His current research interests include saliency detection, face photo-sketch synthesis and deep learning.

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Kong, X., Bi, H., Lu, D. et al. Construction of a Class of Logistic Chaotic Measurement Matrices for Compressed Sensing. Pattern Recognit. Image Anal. 29, 493–502 (2019). https://doi.org/10.1134/S105466181903012X

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