Solving Electrical Impedance Tomography with Deep Learning

Abstract

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.

arXiv comment22 pages, 17 figures

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• An overview on deep learning-based approximation methods for partial differential equations
• Solving inverse problems using conditional invertible neural networks
• Learning nonlocal constitutive models with neural networks
• Meta-learning Pseudo-differential Operators with Deep Neural Networks
• Convergence Rates for Learning Linear Operators from Noisy Data
• Operator Learning Using Random Features: A Tool for Scientific Computing
• A Two-Stage Imaging Framework Combining CNN and Physics-Informed Neural Networks for Full-Inverse Tomography: A Case Study in Electrical Impedance Tomography (EIT)
• Solving Optical Tomography with Deep Learning
• On Reconstruction of Binary Images by Efficient Sample-based Parameterization in Applications for Electrical Impedance Tomography
• Construct Deep Neural Networks Based on Direct Sampling Methods for Solving Electrical Impedance Tomography
• Solver-in-the-Loop joint operator learning: fractional Laplace-Beltrami features for interface reconstruction
• Optimizing electrode positions in 2D Electrical Impedance Tomography using deep learning