Fractional Spectral Graph Wavelets and Their Applications

Wu, Jiasong; Wu, Fuzhi; Yang, Qihan; Zhang, Yan; Liu, Xilin; Kong, Youyong; Senhadji, Lotfi; Hu, Shu

doi:10.1155/2020/2568179

Cited by 13 publications

(10 citation statements)

References 83 publications

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“…where R = Λ a and Λ is the eigenvalue matrix of the Laplacian matrix L G , and more details about GFSO can be found in [31,32].…”

Section: Graph Fractional Fourier Transform (Gfrft)mentioning

confidence: 99%

Optimal Fractional Fourier Filtering in Time-vertex Graphs signal processing

Ge¹,

Guo²,

Wang³

et al. 2022

Preprint

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Graph signal processing (GSP) is an effective tool in dealing with data residing on irregular domains. In GSP, the optimal graph filter is one of the essential techniques, owing to its ability to recover the original signal from the distorted and noisy version. However, most current research focuses on static graph signals and ordinary space/time or frequency domains. The time-varying graph signals have a strong ability to capture the features of real-world data, and fractional domains can provide a more suitable space to separate the signal and noise. In this paper, the optimal time-vertex graph filter and its Wiener-Hopf equation are developed, using the product graph framework. Furthermore, the optimal time-vertex graph filter in fractional domains is also developed, using the graph fractional Laplacian operator and graph fractional Fourier transform.Numerical simulations on real-world datasets will demonstrate the superiority of the optimal time-vertex graph filter in fractional domains over the optimal time-vertex graph filter in ordinary domains and the optimal static graph filter in fractional domains.

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“…where R = Λ a and Λ is the eigenvalue matrix of the Laplacian matrix L G , and more details about GFSO can be found in [31,32].…”

Section: Graph Fractional Fourier Transform (Gfrft)mentioning

confidence: 99%

Optimal Fractional Fourier Filtering in Time-vertex Graphs signal processing

Ge¹,

Guo²,

Wang³

et al. 2022

Preprint

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show abstract

“…The spectral graph Fractional Fourier Transform (SGFRFT) of any signal f building on the graph G is defined by [10]:…”

Section: Spectral Graph Fractional Fourier Transformmentioning

confidence: 99%

“…The main contributions include wavelet and Fourier transforms [5,[7][8][9][10], sam-pling and reconstruction of graph signals [11][12][13][14][15], uncertainty principles [16,17], filtering of graph signals [18,19], etc. Different transforms of graph signal are still the core of GSP.…”

Section: Introductionmentioning

confidence: 99%

“…In order to extract the local information of the graph signal, a new research direction has been proposed in graph signal processing (GSP), that is, fractional order [9,10,[23][24][25]. The fractional order has gained considerable attention in the last 20 years in classical signal processing, and the application of fractional order to graphs has also aroused the interest of researchers.…”

Section: Introductionmentioning

confidence: 99%

“…The graph fractional Fourier transform (GFRFT) related to graph adjacency matrix is proposed in [9]. Furthermore, a new spectral graph Fractional Fourier Transform (SGFRFT) related to graph Laplacian matrix is proposed in [10]. GFRFT and SGFRFT show advantages in revealing the local characteristics of the graph signal.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spectral graph fractional Fourier transform for directed graphs and its application

Yan¹,

Li²

2022

Preprint

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In graph signal processing, most studies assume that the underlying network is undirected. Although the digraph model is rarely adopted, it is more appropriate for many applications, especially for real world networks. In this paper, we present a general framework for extending the graph signal processing to directed graphs in graph fractional domain. For this purpose, we consider a new definition for fractional Laplacian matrix on directed graph and generalize the spectral graph fractional Fourier transform to directed graph (DGFRFT).Based on our new transform, we then define filtering.

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The Optimal Joint Time-Vertex Graph Filter Design: From Ordinary Graph Fourier Domains to Fractional Graph Fourier Domains

Guo

Wang

et al. 2023

Circuits Syst Signal Process

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Fractional Spectral Graph Wavelets and Their Applications

Cited by 13 publications

References 83 publications

Optimal Fractional Fourier Filtering in Time-vertex Graphs signal processing

Optimal Fractional Fourier Filtering in Time-vertex Graphs signal processing

Spectral graph fractional Fourier transform for directed graphs and its application

The Optimal Joint Time-Vertex Graph Filter Design: From Ordinary Graph Fourier Domains to Fractional Graph Fourier Domains

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