Porting Signal Processing from Undirected to Directed Graphs: Case Study Signal Denoising with Unrolling Networks

Directionality is an essential feature of many real-world networks, but problematic in graph signal processing (GSP) because there is no obvious choice of Fourier basis. In this work we investigate how to port GSP methods from undirected to directed graphs using recent work on graph signal denoising using trainable networks as a case study. We consider five notions of directed Fourier bases from the literature and different approaches for porting, from ad-hoc to conceptual. Our experimental results show that directionality does matter, the importance of a shift operator related to the chosen basis, and which directed Fourier basis may be best suited for applications. The best variant also provides a promising method for denoising signals on directed graphs.