Learning Nonlinear Electrical Impedance Tomography

Electrical impedance tomography (EIT) is the problem of determining the electrical conductivity distribution of an unknown medium by making voltage and current measurements at the boundary of the object. The image reconstruction inverse problem of EIT is a nonlinear and severely ill-posed problem. The non-linear approach to this challenging problem commonly relies on the iterative regularized Gauss-Newton method, which, however, has several drawbacks: the critical choice of the regularization matrix and parameter and the difficulty in reconstructing solution step changes, as smooth solutions are favored. We address these problems by learning a data-adaptive neural network as the regularization functional and integrating a local anisotropic total variation layer as an attention-like function into an unrolled Gauss-Newton network. We finally show that the proposed learned non-linear EIT approach strengthen the Gauss-Newton approach providing robust and qualitatively superior reconstructions.