Fractional spectral graph wavelets and their applications

TL;DR

This paper introduces a generalized spectral graph fractional wavelet transform (SGFRWT) based on the fractional Fourier transform, providing a new tool for analyzing signals on weighted graphs with potential applications in graph signal processing.

Contribution

The paper extends the spectral graph wavelet transform by incorporating fractional Fourier transforms, offering a novel and flexible approach for graph signal analysis.

Findings

Developed the spectral graph fractional wavelet transform (SGFRWT)

Derived a fast Fourier series approximation algorithm for SGFRWT

Presented potential applications in graph signal processing

Abstract

One of the key challenges in the area of signal processing on graphs is to design transforms and dictionaries methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier transform (GFT) to graph fractional Fourier transform (GFRFT), 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. The potential applications of SGFRWT are also presented.