Solving electrical impedance tomography with deep learning

DOI10.1016/j.jcp.2019.109119zbMath1453.65041arXiv1906.03944OpenAlexW2948801778WikidataQ126805744 ScholiaQ126805744MaRDI QIDQ2223016

Yu-Wei Fan, Lexing Ying

Publication date: 28 January 2021

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.03944

zbMATH Keywords

inverse problemneural networkselectrical impedance tomographyDirichlet-to-Neumann mapconvolutional neural networkBCR-net

Mathematics Subject Classification ID

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

Related Items (18)

Solving inverse problems using conditional invertible neural networks ⋮ Meta-learning pseudo-differential operators with deep neural networks ⋮ On reconstruction of binary images by efficient sample-based parameterization in applications for electrical impedance tomography ⋮ Machine learning enhanced electrical impedance tomography for 2D materials ⋮ Electrical impedance tomography with deep Calderón method ⋮ Convergence Rates for Learning Linear Operators from Noisy Data ⋮ A high order discontinuous Galerkin method for the recovery of the conductivity in electrical impedance tomography ⋮ Solving inverse problems with deep learning ⋮ On mathematical modeling in image reconstruction and beyond ⋮ An overview on deep learning-based approximation methods for partial differential equations ⋮ Linearized inverse Schrödinger potential problem with partial data and its deep neural network inversion ⋮ Application of a class of iterative algorithms and their accelerations to Jacobian-based linearized EIT image reconstruction ⋮ Non-cooperative finite element games ⋮ The Random Feature Model for Input-Output Maps between Banach Spaces ⋮ Construct Deep Neural Networks based on Direct Sampling Methods for Solving Electrical Impedance Tomography ⋮ Multilevel Fine-Tuning: Closing Generalization Gaps in Approximation of Solution Maps under a Limited Budget for Training Data ⋮ Strong Solutions for PDE-Based Tomography by Unsupervised Learning ⋮ Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning

Uses Software

• TensorFlow
• Keras
• ImageNet
• PDE-Net
• AlexNet

Cites Work

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