Manifold Rewiring for Unlabeled Imaging

TL;DR

This paper introduces a graph denoising method using link-prediction neural networks to improve the quality of neighborhood graphs in noisy imaging data, enhancing downstream analysis tasks.

Contribution

It proposes a novel graph denoising approach based on link prediction neural networks specifically for neighborhood graphs in imaging inverse problems.

Findings

Improves graph quality in synthetic and real noisy data

Enhances performance of vector diffusion maps in cryo-EM

Addresses missing and spurious links in real-world graphs

Abstract

Geometric data analysis relies on graphs that are either given as input or inferred from data. These graphs are often treated as "correct" when solving downstream tasks such as graph signal denoising. But real-world graphs are known to contain missing and spurious links. Similarly, graphs inferred from noisy data will be perturbed. We thus define and study the problem of graph denoising, as opposed to graph signal denoising, and propose an approach based on link-prediction graph neural networks. We focus in particular on neighborhood graphs over point clouds sampled from low-dimensional manifolds, such as those arising in imaging inverse problems and exploratory data analysis. We illustrate our graph denoising framework on regular synthetic graphs and then apply it to single-particle cryo-EM where the measurements are corrupted by very high levels of noise. Due to this degradation, the initial graph is contaminated by noise, leading to missing or spurious edges. We show that our proposed graph denoising algorithm improves the state-of-the-art performance of multi-frequency vector diffusion maps.