JOURNAL OF CHINA UNIVERSITIES OF POSTS AND TELECOM ›› 2018, Vol. 25 ›› Issue (6): 74-80.doi: 10.19682/j.cnki.1005-8885.2018.1029

• Signal Processing • Previous Articles     Next Articles

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).

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

CLC Number: