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Distributed Conjugate Gradient Algorithm for Signal Reconstruction of MOSGFBs

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Abstract

In this paper, we investigate the signal reconstruction of M-channel oversampled graph filter banks (MOSGFBs) on sparse graphs. The analysis filter bank of MOSGFBs can be in polynomial or node-variant (NV) form. Given the analysis filter bank and sampling matrix, the synthesis procedure can be formulated into a quadratic optimization problem. To solve this problem, a novel distributed conjugate gradient (DCG) algorithm is proposed, in which the step size and increment involved in the conjugate gradient iteration are evaluated in a distributed manner. The local step sizes and increments are first calculated using data from neighboring nodes, and then patched to participate in the iteration. The DCG algorithm involves the exchange of information between neighboring nodes and executes the synthesis computation locally; therefore, the synthesis procedure has a low implementation complexity and is suitable for processing large-scale datasets. Numerical examples conducted on synthetic and real-world datasets demonstrate the effectiveness of the proposed algorithm.

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The data used to support the findings of this study are available in [2, 9, 12, 13, 15, 16, 20].

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Funding

This work is supported in part by the National Natural Science Foundation of China (Grant No. 62171146), 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) and by the Innovation Project of GUET Graduate Education (Grant No. 2022YCXS039).

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Author notes

  1. Xinyi Liu and Junzheng Jiang are contributed equally to this work.

Authors and Affiliations

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

    Xinyi Liu, Mou Ma & Junzheng Jiang

  2. Hangzhou Institute of Technology, Xidian University, Hangzhou, 311231, China

    Junzheng Jiang

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  1. Xinyi Liu
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  2. Mou Ma
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  3. Junzheng Jiang
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Correspondence to Mou Ma.

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Liu, X., Ma, M. & Jiang, J. Distributed Conjugate Gradient Algorithm for Signal Reconstruction of MOSGFBs. Circuits Syst Signal Process 43, 1823–1838 (2024). https://doi.org/10.1007/s00034-023-02541-w

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