# Solving Electrical Impedance Tomography with Deep Learning

arXiv: https://arxiv.org/abs/1906.03944 · HTML: https://mlsanity.com/paper/1906.03944/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2019.

## Built on by (most cited first, 18 of 18)

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- [Electrical Impedance Tomography with Deep Calder'on Method](https://mlsanity.com/paper/2304.09074/) (2023)
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- [A Two-Stage Imaging Framework Combining CNN and Physics-Informed Neural Networks for Full-Inverse Tomography: A Case Study in Electrical Impedance Tomography (EIT)](https://mlsanity.com/paper/2407.17721/) (2024)
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- [Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approaches](https://mlsanity.com/paper/2310.18636/) (2023)
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- [Energy stable neural network for gradient flow equations](https://mlsanity.com/paper/2309.10002/) (2023)
- [Multi-Scale Frequency-Enhanced Deep D-bar Method for Electrical Impedance Tomography](https://mlsanity.com/paper/2407.03335/) (2024)
- [A DeepONet for inverting the Neumann-to-Dirichlet Operator in Electrical Impedance Tomography: An approximation theoretic perspective and numerical results](https://mlsanity.com/paper/2407.17182/) (2024)
- [Physics-Encoded Inverse Modeling for Arctic Snow Depth Estimation](https://mlsanity.com/paper/2601.17074/) (2026)

## Abstract (arXiv)

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.