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. Although the directed graph model is rarely adopted, it is more appropriate for many applications, especially 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 definition 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 define 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.