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arXiv · 2506.03925

SVD-Based Graph Fractional Fourier Transform on Directed Graphs and Its Application

Lu Li·Muhan Wang·Haiye Huo
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Abstract

Real-world signals frequently reside on directed Cartesian product graphs, including digital images, sensor networks, and meteorological temperature records. Designing a transform method suitable for processing such multi-dimensional graph signals within the fractional Fourier transform domain remains a critical challenge in graph signal processing (GSP). This paper proposes two novel graph fractional Fourier transforms (GFRFTs) for multi-dimensional signals defined on such directed product graphs and comprehensively investigates their denoising capabilities. Our contributions are fourfold: (1) We propose two distinct two-dimensional GFRFTs based on singular value decompositions of some fractional Laplacian matrices; (2) We generalize these transforms to multi-dimensional graph fractional Fourier transforms (MGFRFTs), establishing a powerful fractional domain analysis framework for multi-dimensional GSP; (3) We investigate the signal reconstruction capability of our proposed GFRFTs, as well as their computational complexity; and (4) We validate the practical utility of our approach through denoising experiments on real-world meteorological temperature datasets.

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Lu Li, Muhan Wang, Haiye Huo. 2025-06-04. SVD-Based Graph Fractional Fourier Transform on Directed Graphs and Its Application. https://arxiv.org/abs/2506.03925

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