Fractional Spectral Graph Wavelets and Their Applications

Jiasong Wu (1, 2, 3) , Fuzhi Wu (3) , Qihan Yang (3) , Yan Zhang (3) , Xilin Liu (4) , Youyong Kong (1, 3) , Lotfi Senhadji (2, 1) , Huazhong Shu (1, 3)

1 CRIBS - Centre de Recherche en Information Biomédicale sino-français
2 LTSI - Laboratoire Traitement du Signal et de l'Image
3 LIST - Laboratory of Image Science and Technology [Nanjing]
4 Taiyuan University of Technology

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 SGFRWTare also presented.

Domains: Engineering Sciences [physics]; Signal and Image processing; Life Sciences [q-bio]; Bioengineering; Imaging

Jiasong Wu, Fuzhi Wu, Qihan Yang, Yan Zhang, Xilin Liu, et al.. Fractional Spectral Graph Wavelets and Their Applications. Mathematical Problems in Engineering, 2020, 2020, pp.1 - 18. ⟨10.1155/2020/2568179⟩. ⟨hal-03004381⟩