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Local-Set-Based Graph Signal Sampling and Reconstruction

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Vertex-Frequency Analysis of Graph Signals

Part of the book series: Signals and Communication Technology ((SCT))

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Abstract

For a graph signal in the low-frequency subspace, the missing data can be reconstructed through the sampled data by exploiting the smoothness of the graph signal. In this chapter, the concepts of local set and centerless local set are introduced and several iterative methods are presented to reconstruct bandlimited graph signal from decimated data or measured signal. These algorithms are built on frame theory and the concepts of (centerless) local sets, based on which several frames and contraction operators are provided. We then prove that the reconstruction methods converge to the original signal under certain conditions and demonstrate the new methods lead to a significantly faster convergence compared with the baseline method. Furthermore, the correspondence between graph signal sampling and time-domain irregular sampling is analyzed comprehensively, which may be helpful to future works on graph signals. Numerical experimental results demonstrate the effectiveness of the reconstruction methods in various sampling geometries, imprecise priori knowledge of cutoff frequency, and noisy scenarios.

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Notes

  1. 1.

    The MATLAB codes for the proposed methods and all experiments are available at http://gu.ee.tsinghua.edu.cn/publications.

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Acknowledgements

This work was funded by the National Natural Science Foundation of China (NSFC 61571263 and NSFC 61531166005), the National Key Research and Development Program of China (Project No. 2016YFE0201900 and 2017YFC0403600), and Tsinghua University Initiative Scientific Research Program (Grant 2014Z01005).

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Authors and Affiliations

  1. Department of Electronic Engineering, Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing, 100084, China

    Yuantao Gu

  2. Huawei Corp., Shanghai, China

    Xiaohan Wang

Authors
  1. Yuantao Gu
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  2. Xiaohan Wang
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Correspondence to Yuantao Gu .

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Editors and Affiliations

  1. Faculty of Electrical Engineering, University of Montenegro, Podgorica, Montenegro

    Ljubiša Stanković

  2. Department of Electrical and Computer Engineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    Ervin Sejdić

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Gu, Y., Wang, X. (2019). Local-Set-Based Graph Signal Sampling and Reconstruction. In: Stanković, L., Sejdić, E. (eds) Vertex-Frequency Analysis of Graph Signals. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-03574-7_7

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  • DOI: https://doi.org/10.1007/978-3-030-03574-7_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03573-0

  • Online ISBN: 978-3-030-03574-7

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