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Operator-based graph linear canonical transform
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DOI：10.1016/j.jfranklin.2025.107877.png)
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Abstract
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This paper proposes a novel graph linear canonical transform framework based on hyper-differential operators, referred to as OGLCT. First, the relationship between the graph fractional Fourier transform (GFrFT) and the graph Fourier transform (GFT) is analyzed, and hyper-differential operators associated with the GFT matrix are derived through solutions to the Sylvester equation. Using these operators, the GFrFT, graph scaling, and graph chirp modulation are defined, culminating in the formal definition of the OGLCT and its fundamental properties. Next, the implementation of the OGLCT is discussed, and parameter optimization techniques are explored. Finally, the application of the OGLCT for feature extraction in image processing is explored, and its effectiveness in image classification tasks is investigated. By adjusting the parameters of the OGLCT, it is demonstrated that flexible tuning significantly enhances model performance, enabling more effective and versatile applications.
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