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CGD-Based Inpainting Algorithm for Time-Varying Signals on Strong Product Graph

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Abstract

A multi-dimensional signal on graph has different features along different directions/dimensions. For example, image signal is isotropic along horizontal and vertical directions, and time-varying signal presents different correlation characters in the time and vertex domains. Nevertheless, the current graph signal processing concentrates on the single shift, which makes it difficult to differentiate the correlation features along different directions. In this paper, we define a multi-shift notion for the time-varying signals on graphs enabling us to separately analyze the multi-dimensional signal along different directions captured by diverse shifts. Furthermore, the multi-shift notion is leveraged to formulate the inpainting problem for time-varying signals on the strong product graph, which can be exploited to characterize three different kinds of elements interaction of time-varying signals by using three different kinds of shifts. The conjugate gradient descent algorithm is further deployed to solve the inpainting problem. Numerical experiments conducted on the synthetic signal and real-world data show the potentiality of the multi-shift representation and the effectiveness of the inpainting algorithm.

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Data Availability

The data used to support the findings of this study are available in [2, 16, 21, 22, 26, 27, 32].

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Funding

This work is supported in part by the National Natural Science Foundation of China (Grant Nos. 62171146, 62261014), by the Guangxi Natural Science Foundation for Distinguished Young Scholar (Grant No. 2021GXNSFFA220004), by the Guangxi special fund project for innovation-driven development (Grant No. GuikeAA21077008), by the Guangxi Science and Technology Base and Talent Special Project (Grant No. Guike AD21220112), by the Dean Project of Guangxi Wireless Broadband Communication and Signal Processing Key Laboratory (Grant No. GXKL06220107), by the Innovation Project of Guangxi Graduate Education (Grant No. YCBZ2023137).

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Author notes

  1. Mou Ma and Junzheng Jiang have contributed equally to this work.

Authors and Affiliations

  1. School of Information and Communication, Guilin University of Electronic Technology, Guilin, 541004, China

    Mou Ma, Junzheng Jiang & Fang Zhou

  2. Guangxi Wireless Broadband Communication and Signal Processing Key Laboratory, Guilin University of Electronic Technology, Guilin, 541004, China

    Fang Zhou

  3. School of Information Engineering, China Jiliang University, Hangzhou, 310018, China

    Fang Zhou

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  1. Mou Ma
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  2. Junzheng Jiang
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Correspondence to Fang Zhou.

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Ma, M., Jiang, J. & Zhou, F. CGD-Based Inpainting Algorithm for Time-Varying Signals on Strong Product Graph. Circuits Syst Signal Process 43, 457–469 (2024). https://doi.org/10.1007/s00034-023-02483-3

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