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Iterative alternating optimization of bi-orthogonal two-channel graph filter bank

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Abstract

The iterative alternating optimization (IAO) algorithm is proposed to optimize the coefficients of the (frequency domain/ spectral) general design two-channel bi-orthogonal graph filter banks (2c-BiO-graph-FB). Its basic idea is iteratively and alternatingly optimizing part of the coefficients while fixing the other coefficients as constants. By utilizing this scheme, the original non-convex optimization design problem is transformed into a series of convex optimization problems. Simulation experiment is conducted to verify the proposed algorithm. The results reveal that the proposed design is an effective one if the order of the graph filter is low. For the low order case, the proposed design can have the smallest frequency selectivity error while simultaneously having exceedingly small reconstruction error (\(\le {10}^{-11}\)). Additionally, as a kind of optimization algorithm, it outperforms the existing trust-region-iterative-gradient-searching (TR-IGS) in terms of the reconstruction error and/or the frequency selectivity error. Further, it can also be utilized to effectively optimize the frequency selectivity of two kinds of special design 2c-BiO-graph-FBs which inherently have exceedingly small reconstruction error. Finally, the designed 2c-BiO-graph-FB by the proposed algorithm is applied to two different specific graphs to decompose and synthesize the corresponding graph signals.

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Funding

This work was supported in part by the National Natural Science Foundation of China under Grant 61601153.

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Authors and Affiliations

  1. School of Communication Engineering, Hangzhou Dianzi University, Hangzhou City, Zhejiang Province, People’s Republic of China

    Hao Wang, Yi Ou, Guangqiu Li & Xueyi Ye

  2. School of Information Engineering, Huzhou University, Huzhou City, Zhejiang Province, People’s Republic of China

    Xinmin Cheng

  3. Zhejiang Lab, Hangzhou City, Zhejiang Province, People’s Republic of China

    Chengwei Huang

Authors
  1. Hao Wang
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  2. Yi Ou
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  3. Xinmin Cheng
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  4. Guangqiu Li
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  5. Xueyi Ye
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  6. Chengwei Huang
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Contributions

Hao Wang wrote the main manuscript text and prepared some of the figures and tables, Yi Ou prepared some of the figures and tables, Xinmin Cheng, Guangqiu Li and Xueyi Ye gave constructive suggestions on Section 6, and Chengwei Huang gave constructive suggestions on Sect. 5.2. All authors reviewed the manuscript.

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Correspondence to Hao Wang.

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Wang, H., Ou, Y., Cheng, X. et al. Iterative alternating optimization of bi-orthogonal two-channel graph filter bank. Multidim Syst Sign Process 34, 447–478 (2023). https://doi.org/10.1007/s11045-023-00868-w

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  • DOI: https://doi.org/10.1007/s11045-023-00868-w

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