中国邮电高校学报(英文版)

中国邮电高校学报(英文版) ›› 2018, Vol. 25 ›› Issue (6): 74-80.doi: 10.19682/j.cnki.1005-8885.2018.1029

• Signal processing • 上一篇    下一篇

Construction of compressed sensing matrices based on affine symplectic space over finite fields

Wang Gang, Niu Minyao, Fu Fangwei   

  1. 1. Chern Institute of Mathematics and Lab of Pure Mathematics and Combinatorics, Nankai University, Tianjin 300071, China
    2. College of Science, Civil Aviation University of China, Tianjin 300300, China
  • 收稿日期:2018-03-21 修回日期:2019-01-02 出版日期:2018-12-30 发布日期:2019-02-26
  • 通讯作者: Wang Gang, E-mail: gwang06080923@mail.nankai.edu.cn E-mail:gwang06080923@mail.nankai.edu.cn
  • 作者简介:Wang Gang, E-mail: gwang06080923@mail.nankai.edu.cn
  • 基金资助:
    This work was supported by the National Basic Research Program of China ( 2013CB834204 ), the National Natural Science Foundation of China (61571243), the Fundamental Research Funds for the Central Universities of China and the Ph. D. Candidate Research Innovation Fund of Nankai University (91822144).

Construction of compressed sensing matrices based on affine symplectic space over finite fields

Wang Gang, Niu Minyao, Fu Fangwei   

  1. 1. Chern Institute of Mathematics and Lab of Pure Mathematics and Combinatorics, Nankai University, Tianjin 300071, China
    2. College of Science, Civil Aviation University of China, Tianjin 300300, China
  • Received:2018-03-21 Revised:2019-01-02 Online:2018-12-30 Published:2019-02-26
  • Contact: Wang Gang, E-mail: gwang06080923@mail.nankai.edu.cn E-mail:gwang06080923@mail.nankai.edu.cn
  • About author:Wang Gang, E-mail: gwang06080923@mail.nankai.edu.cn
  • Supported by:
    This work was supported by the National Basic Research Program of China ( 2013CB834204 ), the National Natural Science Foundation of China (61571243), the Fundamental Research Funds for the Central Universities of China and the Ph. D. Candidate Research Innovation Fund of Nankai University (91822144).

摘要： The compressed sensing matrices based on affine symplectic space are constructed. Meanwhile, a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. Moreover, we merge our binary matrices with other low coherence matrices such as Hadamard matrices and discrete fourier transform (DFT) matrices using the embedding operation. In the numerical simulations, our matrices and modified matrices are superior to Gaussian matrices and DeVore's matrices in the performance of recovering original signals.

关键词: compressed sensing, coherence, sparsity, affine symplectic space, finite fields

Abstract: The compressed sensing matrices based on affine symplectic space are constructed. Meanwhile, a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. Moreover, we merge our binary matrices with other low coherence matrices such as Hadamard matrices and discrete fourier transform (DFT) matrices using the embedding operation. In the numerical simulations, our matrices and modified matrices are superior to Gaussian matrices and DeVore's matrices in the performance of recovering original signals.

Key words: compressed sensing, coherence, sparsity, affine symplectic space, finite fields

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