Wiener Filtering in Joint Time-Vertex Fractional Fourier Domains
Tuna Alikaşifoğlu, Bünyamin Kartal, Aykut Koç
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 timevertex Fourier transform provide a basis to endeavor such timevarying 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.