Fractional Spectral Graph Wavelets and Their Applications

Fractional Spectral Graph Wavelets and Their Applications

One of the key challenges in the area of signal processing on graphs is to design transforms and dictionary methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier transform (GFT) to spectral graph fractional Fourier transform (SGFRFT...

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Main Authors: Jiasong Wu, Fuzhi Wu, Qihan Yang, Yan Zhang, Xilin Liu, Youyong Kong, Lotfi Senhadji, Huazhong Shu
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2020/2568179
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spelling doaj-06d6e68697844e6f90a9e3c4dd1e3ad02020-11-25T04:00:55ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/25681792568179Fractional Spectral Graph Wavelets and Their ApplicationsJiasong Wu0Fuzhi Wu1Qihan Yang2Yan Zhang3Xilin Liu4Youyong Kong5Lotfi Senhadji6Huazhong Shu7Laboratory of Image Science and Technology (LIST), Key Laboratory of Computer Network and Information Integration, Southeast University, Ministry of Education, Nanjing 210096, ChinaLaboratory of Image Science and Technology (LIST), Key Laboratory of Computer Network and Information Integration, Southeast University, Ministry of Education, Nanjing 210096, ChinaLaboratory of Image Science and Technology (LIST), Key Laboratory of Computer Network and Information Integration, Southeast University, Ministry of Education, Nanjing 210096, ChinaLaboratory of Image Science and Technology (LIST), Key Laboratory of Computer Network and Information Integration, Southeast University, Ministry of Education, Nanjing 210096, ChinaCollege of Data Science, Taiyuan University of Technology, Taiyuan 030024, ChinaLaboratory of Image Science and Technology (LIST), Key Laboratory of Computer Network and Information Integration, Southeast University, Ministry of Education, Nanjing 210096, ChinaUniv Rennes, INSERM, LTSI-UMR 1099, 35042 Rennes, FranceLaboratory of Image Science and Technology (LIST), Key Laboratory of Computer Network and Information Integration, Southeast University, Ministry of Education, Nanjing 210096, ChinaOne of the key challenges in the area of signal processing on graphs is to design transforms and dictionary methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier transform (GFT) to spectral graph fractional Fourier transform (SGFRFT), which is then used to define a novel transform named spectral graph fractional wavelet transform (SGFRWT), which is a generalized and extended version of spectral graph wavelet transform (SGWT). A fast algorithm for SGFRWT is also derived and implemented based on Fourier series approximation. Some potential applications of SGFRWT are also presented.http://dx.doi.org/10.1155/2020/2568179
collection DOAJ
language English
format Article
sources DOAJ
author Jiasong Wu
Fuzhi Wu
Qihan Yang
Yan Zhang
Xilin Liu
Youyong Kong
Lotfi Senhadji
Huazhong Shu
spellingShingle Jiasong Wu
Fuzhi Wu
Qihan Yang
Yan Zhang
Xilin Liu
Youyong Kong
Lotfi Senhadji
Huazhong Shu
Fractional Spectral Graph Wavelets and Their Applications
Mathematical Problems in Engineering
author_facet Jiasong Wu
Fuzhi Wu
Qihan Yang
Yan Zhang
Xilin Liu
Youyong Kong
Lotfi Senhadji
Huazhong Shu
author_sort Jiasong Wu
title Fractional Spectral Graph Wavelets and Their Applications
title_short Fractional Spectral Graph Wavelets and Their Applications
title_full Fractional Spectral Graph Wavelets and Their Applications
title_fullStr Fractional Spectral Graph Wavelets and Their Applications
title_full_unstemmed Fractional Spectral Graph Wavelets and Their Applications
title_sort fractional spectral graph wavelets and their applications
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2020-01-01
description One of the key challenges in the area of signal processing on graphs is to design transforms and dictionary methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier transform (GFT) to spectral graph fractional Fourier transform (SGFRFT), which is then used to define a novel transform named spectral graph fractional wavelet transform (SGFRWT), which is a generalized and extended version of spectral graph wavelet transform (SGWT). A fast algorithm for SGFRWT is also derived and implemented based on Fourier series approximation. Some potential applications of SGFRWT are also presented.
url http://dx.doi.org/10.1155/2020/2568179
work_keys_str_mv AT jiasongwu fractionalspectralgraphwaveletsandtheirapplications
AT fuzhiwu fractionalspectralgraphwaveletsandtheirapplications
AT qihanyang fractionalspectralgraphwaveletsandtheirapplications
AT yanzhang fractionalspectralgraphwaveletsandtheirapplications
AT xilinliu fractionalspectralgraphwaveletsandtheirapplications
AT youyongkong fractionalspectralgraphwaveletsandtheirapplications
AT lotfisenhadji fractionalspectralgraphwaveletsandtheirapplications
AT huazhongshu fractionalspectralgraphwaveletsandtheirapplications
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