Graph Neural Net using Analytical Graph Filters and Topology Optimization for Image Denoising

TL;DR

This paper introduces a graph neural network for image denoising that uses analytically defined graph filters and topology optimization, achieving comparable or better performance than CNNs without requiring filter training.

Contribution

The paper presents a novel GNN architecture employing analytically defined graph filters and topology optimization, eliminating the need for filter training and enhancing interpretability.

Findings

Achieves image denoising performance comparable to state-of-the-art CNNs.

Outperforms CNNs by over 1dB PSNR when training and testing data differ.

Provides an interpretable, analytically defined filtering approach.

Abstract

While convolutional neural nets (CNNs) have achieved remarkable performance for a wide range of inverse imaging applications, the filter coefficients are computed in a purely data-driven manner and are not explainable. Inspired by an analytically derived CNN by Hadji et al., in this paper we construct a new layered graph neural net (GNN) using GraphBio as our graph filter. Unlike convolutional filters in previous GNNs, our employed GraphBio is analytically defined and requires no training, and we optimize the end-to-end system only via learning of appropriate graph topology at each layer. In signal filtering terms, it means that our linear graph filter at each layer is always intrepretable as low-pass with known biorthogonal conditions, while the graph spectrum itself is optimized via data training. As an example application, we show that our analytical GNN achieves image denoising performance comparable to a state-of-the-art CNN-based scheme when the training and testing data share the same statistics, and when they differ, our analytical GNN outperforms it by more than 1dB in PSNR.