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Research on Construction of Measurement Matrix Based on Welch Bound

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Communications and Networking (ChinaCom 2020)

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Abstract

Compressive sensing (CS) is a new theory of data acquisition and reconstruction. It permits the data of interest being sampled at a sub-Nyquist rate, meanwhile still allowing perfect reconstruction of data from highly incomplete measurements. During this process, the construction of measurement matrix is undoubtedly the key point. However, the traditional random measurement matrices, though having good performance, are difficult to implement in hardware and lack the ability of dealing with large signals. In this paper, we construct a series of novel measurement matrices (HWKM and HWCM) based on Welch bound, by sifting the basis matrix based on Hadamard matrix. Therefore, the proposed matrices are deterministic measurement, which can be easily designed in hardware. Specially, it is proved to have low coherence, which can even approach to Welch bound. Experimental results show that the proposed matrices, compared with traditional measurement matrices, not only have considerable reconstruction performance in terms of reconstruction error and the signal-to-noise ratio, but also accelerate recovery time.

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Acknowledgements

This paper is supported by NSFC (No. 61372069).

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Authors and Affiliations

  1. State Key Laboratory of Integrated Services Networks(ISN), School of Telecommunications Engineering, Xidian University, Xi’an, China

    Han Zhang, Song Xiao & Hongping Gan

Authors
  1. Han Zhang
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  2. Song Xiao
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  3. Hongping Gan
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Corresponding author

Correspondence to Song Xiao .

Editor information

Editors and Affiliations

  1. Shanghai University, Shanghai, China

    Honghao Gao

  2. Tsinghua University, Beijing, China

    Pingyi Fan

  3. Fudan University, Shanghai, China

    Jun Wun

  4. Tongji University, Shanghai, China

    Xue Xiaoping

  5. Hangzhou Dianzi University, Hangzhou, China

    Jun Yu

  6. Huawei Technologies Co Ltd, Shanghai, China

    Yi Wang

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© 2021 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Zhang, H., Xiao, S., Gan, H. (2021). Research on Construction of Measurement Matrix Based on Welch Bound. In: Gao, H., Fan, P., Wun, J., Xiaoping, X., Yu, J., Wang, Y. (eds) Communications and Networking. ChinaCom 2020. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 352. Springer, Cham. https://doi.org/10.1007/978-3-030-67720-6_48

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  • DOI: https://doi.org/10.1007/978-3-030-67720-6_48

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-67719-0

  • Online ISBN: 978-3-030-67720-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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