Optimal Fractional Fourier Filtering in Time-vertex Graphs signal processing

TL;DR

This paper introduces a novel optimal fractional Fourier filtering method for time-vertex graph signals, enhancing signal recovery in dynamic, irregular data domains by leveraging fractional domains and the product graph framework.

Contribution

It develops the optimal time-vertex graph filter in fractional domains using the fractional Laplacian and Fourier transform, extending beyond static and ordinary domain filters.

Findings

Fractional domain filters outperform ordinary domain filters in real-world data recovery.

The proposed filters demonstrate superior noise separation capabilities.

Numerical simulations confirm the effectiveness of fractional domain filtering.

Abstract

Graph signal processing (GSP) is an effective tool in dealing with data residing in irregular domains. In GSP, the optimal graph filter is one of the essential techniques, owing to its ability to recover the original signal from the distorted and noisy version. However, most current research focuses on static graph signals and ordinary space/time or frequency domains. The time-varying graph signals have a strong ability to capture the features of real-world data, and fractional domains can provide a more suitable space to separate the signal and noise. In this paper, the optimal time-vertex graph filter and its Wiener-Hopf equation are developed, using the product graph framework. Furthermore, the optimal time-vertex graph filter in fractional domains is also developed, using the graph fractional Laplacian operator and graph fractional Fourier transform. Numerical simulations on real-world datasets will demonstrate the superiority of the optimal time-vertex graph filter in fractional domains over the optimal time-vertex graph filter in ordinary domains and the optimal static graph filter in fractional domains.