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Time-Varying Graph Signals Reconstruction

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Book cover Vertex-Frequency Analysis of Graph Signals

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

Abstract

Signal processing on graphs is an emerging research field dealing with signals living on an irregular domain that is captured by a graph, and has been applied to sensor networks, machine learning, climate analysis, et cetera. Existing works on sampling and reconstruction of graph signals mainly studied static bandlimited signals. However, many real-world graph signals are time-varying, and they evolve smoothly, so instead of the signals themselves being bandlimited or smooth on graph, it is more reasonable that their temporal differences are smooth on graph. In this chapter, two new batch reconstruction methods of time-varying graph signals are proposed by exploiting the smoothness of the temporal difference signals, and the uniqueness as well as the reconstruction error bound of the solutions to the corresponding optimization problems are theoretically analyzed. Furthermore, driven by practical applications faced with real-time requirements, huge size of data, lack of computing center, or communication difficulties between two non-neighboring vertices, an online distributed method is proposed by applying local properties of the temporal difference operator and the graph Laplacian matrix. We also highlight the spatio-temporal signals prevalently existing in sociology, climatology, and environmental studies form a special type of time-varying graph signals, and can be reconstructed by the proposed methods. Experiments on a variety of real-world datasets demonstrate the excellent performance of the proposed methods.

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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/codes/Timevarying_GS_Reconstruction.zip.

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

    Xianghui Mao & Yuantao Gu

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  1. Xianghui Mao
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  2. Yuantao Gu
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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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Mao, X., Gu, Y. (2019). Time-Varying Graph Signals 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_8

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  • DOI: https://doi.org/10.1007/978-3-030-03574-7_8

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