Network inpainting via optimal transport

In this work, we present a novel tool for reconstructing transport 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. Under the assumption that such physical information can be properly identified, we demonstrate through a range of numerical tests that our approach can effectively rebuild the primary features of damaged networks, even when artifacts are present.