Spectral graph fractional Fourier transform for directed graphs and its application

In graph signal processing, the underlying network in many studies is assumed to be undirected. Al-though the directed graph model is rarely adopted, it is more appropriate for many applications, espe-cially for real-world networks. In this paper, we present a general framework for extending graph signal processing to directed graphs in the graph fractional domain. For this purpose, we consider a new defini-tion for the fractional Hermitian Laplacian matrix on a directed graph and generalize the spectral graph fractional Fourier transform to the directed graph (DGFRFT). Based on our new transform, we then de-fine filtering, which is used to reduce unnecessary noise superimposed on real data. Finally, the denoising performance of the proposed DGFRFT approach is also evaluated through numerical experiments by using real-world directed graphs. & COPY; 2023 Elsevier B.V. All rights reserved.