Robust Graph Filter Identification and Graph Denoising from Signal Observations

TL;DR

This paper introduces a robust method for graph filter identification and graph denoising that jointly estimates the graph structure and filters from noisy observations, improving accuracy in perturbed graph scenarios.

Contribution

It formulates a novel non-convex optimization approach for joint graph denoising and filter identification, with an efficient algorithm and extensions for multiple filters and reduced complexity.

Findings

The proposed method outperforms existing approaches on synthetic datasets.

It effectively denoises graphs while identifying graph filters.

Numerical results demonstrate robustness against graph perturbations.

Abstract

When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and perturbations. As a result, any method relying on the graph topology may yield suboptimal results if those imperfections are ignored. Motivated by this, we propose a novel approach for handling perturbations on the links of the graph and apply it to the problem of robust graph filter (GF) identification from input-output observations. Different from existing works, we formulate a non-convex optimization problem that operates in the vertex domain and jointly performs GF identification and graph denoising. As a result, on top of learning the desired GF, an estimate of the graph is obtained as a byproduct. To handle the resulting bi-convex problem, we design an algorithm that blends techniques from alternating optimization and majorization minimization, showing its convergence to a stationary point. The second part of the paper i) generalizes the design to a robust setup where several GFs are jointly estimated, and ii) introduces an alternative algorithmic implementation that reduces the computational complexity. Finally, the detrimental influence of the perturbations and the benefits resulting from the robust approach are numerically analyzed over synthetic and real-world datasets, comparing them with other state-of-the-art alternatives.