4.3 Article

Fractional Spectral Graph Wavelets and Their Applications

Journal

MATHEMATICAL PROBLEMS IN ENGINEERING
Volume 2020, Issue -, Pages -

Publisher

HINDAWI LTD
DOI: 10.1155/2020/2568179

Keywords

-

Funding

  1. National Natural Science Foundation of China [61876037, 31800825, 61871117, 61871124, 61773117]
  2. National Science and Technology Major Project of the Ministry of Science and Technology of China [2018ZX10201002-003]
  3. Short-Term Recruitment Program of Foreign Experts [WQ20163200398]
  4. INSERM

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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.

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