Wiener filtering in joint time-vertex fractional Fourier domains

Abstract

Graph signal processing (GSP) uses network structures to analyze and manipulate interconnected signals. These graph signals can also be time-varying. The established joint time-vertex processing framework and corresponding joint time-vertex Fourier transform provide a basis to endeavor such time-varying graph signals. The optimal Wiener filtering problem has been deliberated within the joint time-vertex framework. However, the ordinary Fourier domain is only sometimes optimal for separating the signal and noise; one can achieve lower error rates in a fractional Fourier domain. In this paper, we solve the optimal Wiener filtering problem in the joint time-vertex fractional Fourier domains. We provide a theoretical analysis and numerical experiments with comprehensive comparisons to existing filtering approaches for time-varying graph signals to demonstrate the advantages of our approach.