mlsanityData to 7 Oct 2026

Solving Electrical Impedance Tomography with Deep Learning

arXiv 1906.03944 ↗First posted 6 Jun 2019physics.comp-ph cs.LG cs.NAcited by 18

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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.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Jun 2019.

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Citing papers per year: 2021: 1; 2022: 1; 2023: 5; 2024: 7; 2025: 3; 2026: 1.

18 papers.

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  1. 2021Convergence Rates for Learning Linear Operators from Noisy Datacited by 55
  2. 2022Transformer Meets Boundary Value Inverse Problemscited by 22
  3. 2024Operator Learning Using Random Features: A Tool for Scientific Computingcited by 21
  4. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  5. 2023Manifold Learning by Mixture Models of VAEs for Inverse Problemscited by 16
  6. 2024Paired Autoencoders for Likelihood-free Estimation in Inverse Problemscited by 6
  7. 2023Operator learning for hyperbolic partial differential equationscited by 4
  8. 2023Electrical Impedance Tomography with Deep Calder'on Methodcited by 3
  9. 2024Convergence of Implicit Gradient Descent for Training Two-Layer Physics-Informed Neural Networkscited by 3
  10. 2024A Two-Stage Imaging Framework Combining CNN and Physics-Informed Neural Networks for Full-Inverse Tomography: A Case Study in Electrical Impedance Tomography (EIT)cited by 3
  11. 2023Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approachescited by 2
  12. 2024ODE-DPS: ODE-based Diffusion Posterior Sampling for Inverse Problems in Partial Differential Equationcited by 2
6 more
  1. 2025Learning where to learn: Training data distribution optimization for scientific machine learningcited by 1
  2. 2025Rates and architectures for learning geometrically non-trivial operatorscited by 1
  3. 2023Energy stable neural network for gradient flow equationscited by 0
  4. 2024Multi-Scale Frequency-Enhanced Deep D-bar Method for Electrical Impedance Tomographycited by 0
  5. 2024A DeepONet for inverting the Neumann-to-Dirichlet Operator in Electrical Impedance Tomography: An approximation theoretic perspective and numerical resultscited by 0
  6. 2026Physics-Encoded Inverse Modeling for Arctic Snow Depth Estimationcited by 0