Fractional spectral graph wavelets and their applications
This work addresses a key problem in graph signal processing for researchers and practitioners by providing a novel transform with potential applications, though it appears incremental as it builds upon existing spectral graph wavelet transforms.
The authors tackled the challenge of designing transforms for signal processing on graphs by generalizing the graph Fourier transform to a fractional version and introducing the spectral graph fractional wavelet transform, which extends existing spectral graph wavelet transforms and includes a fast algorithm based on Fourier series approximation.
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.