Imaging conductivity from current density magnitude using neural networks*

Conductivity imaging represents one of the most important tasks in medical imaging. In this work we develop a neural network based reconstruction technique for imaging the conductivity from the magnitude of the internal current density. It is achieved by formulating the problem as a relaxed weighted least-gradient problem, and then approximating its minimizer by standard fully connected feedforward neural networks. We derive bounds on two components of the generalization error, i.e., approximation error and statistical error, explicitly in terms of properties of the neural networks (e.g., depth, total number of parameters, and the bound of the network parameters). We illustrate the performance and distinct features of the approach on several numerical experiments. Numerically, it is observed that the approach enjoys remarkable robustness with respect to the presence of data noise.