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Solving electrical impedance tomography with deep learning. (English) Zbl 1453.65041

Summary: This paper introduces a new approach for solving electrical impedance tomography (EIT) problems using deep neural networks. The mathematical problem of EIT is to invert the electrical conductivity from the Dirichlet-to-Neumann (DtN) map. Both the forward map from the electrical conductivity to the DtN map and the inverse map are high-dimensional and nonlinear. Motivated by the linear perturbative analysis of the forward map and based on a numerically low-rank property, we propose compact neural network architectures for the forward and inverse maps for both 2D and 3D problems. Numerical results demonstrate the efficiency of the proposed neural networks.

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
68T07 Artificial neural networks and deep learning
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
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