Network Inpainting via Optimal Transport

The precise digital reconstruction of natural networks such as blood vessels or plant roots is crucial to ensure the quality ofsimulation-driven predictions.

However, these structures can often be accessed only via noninvasive techniques, leading to artifactsthat compromise the reliability of the data and the derived simulations.

No technological solution is currently able to recover digitalreconstructions of ""real"" networks from corrupted images.The NIOT (Network Inpainting via Optimal Transport) project aims to fill this technological gap by defining for the first time a robustmathematical formulation of the image network reconstruction problem.

Thanks to the most recent advances of the optimaltransport theory, we will finally encode into equations the well-known fact that several natural networks are designed to transportresources with the least effort possible.

We will adopt a variational image processing method, where the reconstructed network isobtained as the density minimizing the sum of the discrepancy with the observed data and a branch inducing functional.

As such, ourproposed methodology builds a bridge between the image regularization and optimal transport communities.A major ambition of the project is to pair the theoretical analysis with robust simulation tools that are capable of handling real dataarising from MRI acquisition techniques.

This will require exploitation and development of dedicated components to handle largedatasets, both from a data handling and a multiscale simulation perspective. Our algorithm will be tested on a sequence ofincreasingly channeling problems.

We will start from simple synthetic networks, then we will use an high-quality map of the bloodvessel network of a mouse brain. The final benchmark will be to reconstruct of corrupted vascular networks in MRI scans of humanpatients.