Untrained Graph Neural Networks for Denoising

A fundamental problem in signal processing is to denoise a signal. While there are many well-performing methods for denoising signals defined on regular domains, including images two-dimensional pixel grid, important classes of over irregular domains that can be conveniently represented by graph. This paper introduces two untrained graph neural network architectures denoising, develops theoretical guarantees their capabilities simple setup, and provides empirical evidence more general scenarios. The differ how they incorporate the information encoded graph, with one relying convolutions other employing upsampling operators based hierarchical clustering. Each architecture implements different prior targeted signals. Finally, we provide numerical experiments synthetic real datasets i) asses behavior predicted our results ii) compare performance existing alternatives.