A Time-Vertex Signal Processing Framework

TL;DR

This paper introduces a comprehensive framework for analyzing time-varying signals on graphs, combining time and graph domain techniques to improve filtering accuracy and enable advanced signal analysis.

Contribution

It formalizes joint harmonic analysis on graphs, enhances joint filtering accuracy, and develops time-vertex dictionaries for multi-scale analysis of dynamic signals.

Findings

Improved joint filtering accuracy by up to two orders of magnitude.

Demonstrated applications in denoising, classification, inpainting, and source localization.

Showed potential benefits for regression and learning tasks.

Abstract

An emerging way to deal with high-dimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work aims to elevate the notion of joint harmonic analysis to a full-fledged framework denoted as Time-Vertex Signal Processing, that links together the time-domain signal processing techniques with the new tools of graph signal processing. This entails three main contributions: (a) We provide a formal motivation for harmonic time-vertex analysis as an analysis tool for the state evolution of simple Partial Differential Equations on graphs. (b) We improve the accuracy of joint filtering operators by up-to two orders of magnitude. (c) Using our joint filters, we construct time-vertex dictionaries analyzing the different scales and the local time-frequency content of a signal. The utility of our tools is illustrated in numerous applications and datasets, such as dynamic mesh denoising and classification, still-video inpainting, and source localization in seismic events. Our results suggest that joint analysis of time-vertex signals can bring benefits to regression and learning.