Graph Iterative Filtering methods for the analysis of nonstationary signals on graphs

TL;DR

This paper extends iterative filtering to graph signals, enabling analysis of non-stationary, non-uniformly sampled data with proven convergence and successful real-world applications.

Contribution

The authors introduce two graph-based iterative filtering algorithms with a unified convergence analysis for non-stationary signals on graphs.

Findings

Algorithms effectively decompose non-stationary graph signals.

Numerical experiments confirm the methods' effectiveness on real-world data.

Proven convergence guarantees for the proposed algorithms.

Abstract

In the analysis of real-world data, extracting meaningful features from signals is a crucial task. This is particularly challenging when signals contain non-stationary frequency components. The Iterative Filtering (IF) method has proven to be an effective tool for decomposing such signals. However, such a technique cannot handle directly data that have been sampled non-uniformly. On the other hand, graph signal processing has gained increasing attention due to its versatility and wide range of applications, and it can handle data sampled both uniformly and non-uniformly. In this work, we propose two algorithms that extend the IF method to signals defined on graphs. In addition, we provide a unified convergence analysis for the different IF variants. Finally, numerical experiments on a variety of graphs, including real-world data, confirm the effectiveness of the proposed methods. In particular, we test our algorithms on seismic data and the total electron content of the ionosphere. Those data are by their nature non-uniformly sampled, and, therefore, they cannot be directly analyzed by the standard IF method.