Untrained Graph Neural Networks for Denoising
This addresses denoising for signals on irregular graph domains, which is important for applications like social networks or sensor data, but it is incremental as it adapts untrained neural network ideas to graphs.
The paper tackles graph signal denoising by introducing two untrained graph neural network architectures, one using graph convolutions and the other graph upsampling, and provides theoretical guarantees and numerical validation on real and synthetic datasets.
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.