Fractional Spectral Graph Wavelets and Their Applications. (6th November 2020)

• Record Type: Journal Article
• Authors: Wu, Jiasong; Wu, Fuzhi; Yang, Qihan; Zhang, Yan; Liu, Xilin; Kong, Youyong; Senhadji, Lotfi; Shu, Huazhong
• Other Names: Smolka Bogdan Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-11-06
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/2568179
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.