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Symmetric Toeplitz-Structured Compressed Sensing Matrices

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Abstract

How to construct a suitable measurement matrix is an important topic in compressed sensing. A significant part of the recent work is that the measurement matrices are not completely random on the entries but exhibit some considerable structures. In this paper, we proved that a symmetric Toeplitz matrix and its variant can be used as measurement matrices and recovery signal with high probability. Compared with random matrices (e.g. Gaussian and Bernoulli matrices) and some structured matrices (e.g. Toeplitz and circulant matrices), we need to generate fewer independent entries to obtain the measurement matrix while the effectiveness of the recovery keeps good.

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Acknowledgments

Supported by National Natural Science Foundation of China (11071002, 11371028), Program for New Century Excellent Talents in University (NCET-10-0001), Key Project of Chinese Ministry of Education (210091), Specialized Research Fund for the Doctoral Program of Higher Education (20103401110002), Scientific Research Fund for Fostering Distinguished Young Scholars of Anhui University(KJJQ1001), Academic Innovation Team of Anhui University Project (KJTD001B), Open Project of Key Laboratory of Opto-Electronic Information Acquisition and Manipulation Ministry of Education (OEIAM201406).

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Authors and Affiliations

  1. Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, Anhui University, Hefei, 230039, People’s Republic of China

    Tao Huang, Yi-Zheng Fan & Ming Zhu

  2. School of Mathematical Sciences, Anhui University, Hefei, 230601, People’s Republic of China

    Tao Huang, Yi-Zheng Fan & Ming Zhu

Authors
  1. Tao Huang
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  2. Yi-Zheng Fan
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  3. Ming Zhu
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Correspondence to Yi-Zheng Fan.

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Huang, T., Fan, YZ. & Zhu, M. Symmetric Toeplitz-Structured Compressed Sensing Matrices. Sens Imaging 16, 7 (2015). https://doi.org/10.1007/s11220-015-0109-0

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  • DOI: https://doi.org/10.1007/s11220-015-0109-0

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