Robust graph-filter identification with graph denoising regularization

TL;DR

This paper introduces a robust method for identifying graph filters that accounts for graph perturbations by jointly denoising the graph and estimating the filter, improving performance in noisy real-world scenarios.

Contribution

It proposes a novel joint graph denoising and filter identification framework formulated as a non-convex optimization problem with relaxations and graph-stationarity assumptions.

Findings

Outperforms existing robust methods in synthetic experiments

Effective on real-world graph datasets

Enhances robustness against graph perturbations

Abstract

When approaching graph signal processing tasks, graphs are usually assumed to be perfectly known. However, in many practical applications, the observed (inferred) network is prone to perturbations which, if ignored, will hinder performance. Tailored to those setups, this paper presents a robust formulation for the problem of graph-filter identification from input-output observations. Different from existing works, our approach consists in addressing the robust identification by formulating a joint graph denoising and graph-filter identification problem. Such a problem is formulated as a non-convex optimization, suitable relaxations are proposed, and graph-stationarity assumptions are incorporated to enhance performance. Finally, numerical experiments with synthetic and real-world graphs are used to assess the proposed schemes and compare them with existing (robust) alternatives.