Two-Dimensional Graph Bi-Fractional Fourier Transform
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917007801188352 |
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| author | Wang, Mingzhi Zhang, Zhichao |
| author_facet | Wang, Mingzhi Zhang, Zhichao |
| contents | Graph signal processing (GSP) advances spectral analysis on irregular domains. However, existing two-dimensional graph fractional Fourier transform (2D-GFRFT) employs a single fractional order for both factor graphs, thereby limiting its adaptability to heterogeneous signals. We proposed the two-dimensional graph bi-fractional Fourier transform (2D-GBFRFT), which assigns independent fractional orders to the factor graphs of a Cartesian product while preserving separability. We established invertibility, unitarity, and index additivity, and developed two filtering schemes: a Wiener-style design through grid search and a differentiable framework that jointly optimizes transform orders and diagonal spectral filters. We further introduced a hybrid interpolation with the joint time-vertex fractional Fourier transform (JFRFT), controlled by a tunable parameter that balances the two methods. In the domains of synthetic Cartesian product graph signals, authentic temporal graph datasets, and dynamic image deblurring, 2D-GBFRFT consistently surpasses 2D-GFRFT and enhances JFRFT. Experimental results confirmed the versatility and superior performance of 2D-GBFRFT for filtering in GSP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11279 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-Dimensional Graph Bi-Fractional Fourier Transform Wang, Mingzhi Zhang, Zhichao Signal Processing Graph signal processing (GSP) advances spectral analysis on irregular domains. However, existing two-dimensional graph fractional Fourier transform (2D-GFRFT) employs a single fractional order for both factor graphs, thereby limiting its adaptability to heterogeneous signals. We proposed the two-dimensional graph bi-fractional Fourier transform (2D-GBFRFT), which assigns independent fractional orders to the factor graphs of a Cartesian product while preserving separability. We established invertibility, unitarity, and index additivity, and developed two filtering schemes: a Wiener-style design through grid search and a differentiable framework that jointly optimizes transform orders and diagonal spectral filters. We further introduced a hybrid interpolation with the joint time-vertex fractional Fourier transform (JFRFT), controlled by a tunable parameter that balances the two methods. In the domains of synthetic Cartesian product graph signals, authentic temporal graph datasets, and dynamic image deblurring, 2D-GBFRFT consistently surpasses 2D-GFRFT and enhances JFRFT. Experimental results confirmed the versatility and superior performance of 2D-GBFRFT for filtering in GSP. |
| title | Two-Dimensional Graph Bi-Fractional Fourier Transform |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2510.11279 |