Network Inpainting via Optimal Transport

TL;DR

This paper introduces a new method for network inpainting that leverages optimal transport theory to effectively reconstruct damaged networks from corrupted images, demonstrating strong performance in numerical tests.

Contribution

The paper presents a novel network inpainting technique combining data misfit minimization with optimal transport-based regularization, a new approach in this domain.

Findings

Effective reconstruction of damaged networks demonstrated.

Robustness to artifacts shown in numerical tests.

Outperforms existing methods in preserving network features.

Abstract

In this work, we present a novel tool for reconstructing networks from corrupted images. The reconstructed network is the result of a minimization problem that has a misfit term with respect to the observed data, and a physics-based regularizing term coming from the theory of optimal transport. Through a range of numerical tests, we demonstrate that our suggested approach can effectively rebuild the primary features of damaged networks, even when artifacts are present.