Untrained Graph Neural Networks for Denoising

TL;DR

This paper introduces two novel untrained graph neural network architectures for denoising signals on irregular graph domains, providing theoretical guarantees and empirical validation of their effectiveness.

Contribution

The paper proposes two untrained GNN architectures for graph signal denoising, with theoretical analysis and experimental validation demonstrating their capabilities.

Findings

Theoretical guarantees established for the denoising performance.

Experimental results show competitive denoising accuracy on real and synthetic data.

Comparison with existing methods highlights the advantages of the proposed architectures.

Abstract

A fundamental problem in signal processing is to denoise a signal. While there are many well-performing methods for denoising signals defined on regular supports, such as images defined on two-dimensional grids of pixels, many important classes of signals are defined over irregular domains such as graphs. This paper introduces two untrained graph neural network architectures for graph signal denoising, provides theoretical guarantees for their denoising capabilities in a simple setup, and numerically validates the theoretical results in more general scenarios. The two architectures differ on how they incorporate the information encoded in the graph, with one relying on graph convolutions and the other employing graph upsampling operators based on hierarchical clustering. Each architecture implements a different prior over the targeted signals. To numerically illustrate the validity of the theoretical results and to compare the performance of the proposed architectures with other denoising alternatives, we present several experimental results with real and synthetic datasets.