Spatial regularization and level-set methods for experimental electrical impedance tomography with partial data

Electrical Impedance Tomography (EIT) aims at reconstructing the electric conductivity distribution in a body from electro-static boundary measurements. The inverse problem is severely ill-posed, especially when only partial data is considered. In this work, we propose three methods for the combined reconstruction and segmentation in EIT with partial data. Firstly, we introduce a regularization that takes spatial information into account and corrects for limited coverage. Secondly, we exploit the Chan–Vese method for improving the segmentation step. Finally, we utilize an optimization framework with a level-set approach to simultaneously reconstruct and segment inclusions. The work is done in the context of the Kuopio Tomography Challenge 2023. We demonstrate on experimental tank data that each of the three methods performs significantly better than a classical linearization approach, especially in partial-data scenarios. In particular, the level-set method drastically improves the reconstruction of inclusions with complicated boundaries; this method is superior among our contributions.