# Deep D-bar: Real time Electrical Impedance Tomography Imaging with Deep Neural Networks

arXiv: https://arxiv.org/abs/1711.03180 · HTML: https://mlsanity.com/paper/1711.03180/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2017.

## Built on by (most cited first, 24 of 24)

- [Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems](https://mlsanity.com/paper/2212.03130/) (2022)
- [Transformer Meets Boundary Value Inverse Problems](https://mlsanity.com/paper/2209.14977/) (2022)
- [Manifold Learning by Mixture Models of VAEs for Inverse Problems](https://mlsanity.com/paper/2303.15244/) (2023)
- [Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems](https://mlsanity.com/paper/2103.15138/) (2021)
- [Paired Autoencoders for Likelihood-free Estimation in Inverse Problems](https://mlsanity.com/paper/2405.13220/) (2024)
- [Electrical Impedance Tomography with Deep Calder'on Method](https://mlsanity.com/paper/2304.09074/) (2023)
- [Domain independent post-processing with graph U-nets: Applications to Electrical Impedance Tomographic Imaging](https://mlsanity.com/paper/2305.05020/) (2023)
- [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)
- [Enhancing Electrical Impedance Tomography reconstruction using Learned Half-Quadratic Splitting Networks with Anderson Acceleration](https://mlsanity.com/paper/2304.14491/) (2023)
- [Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approaches](https://mlsanity.com/paper/2310.18636/) (2023)
- [Diff-INR: Generative Regularization for Electrical Impedance Tomography](https://mlsanity.com/paper/2409.04494/) (2024)
- [Verifying Inverse Model Neural Networks](https://mlsanity.com/paper/2202.02429/) (2022)
- [Physics-Driven Neural Compensation For Electrical Impedance Tomography](https://mlsanity.com/paper/2504.18067/) (2025)
- [Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)](https://mlsanity.com/paper/2204.09815/) (2022)
- [Machine learning for structural design models of continuous beam systems via influence zones](https://mlsanity.com/paper/2403.09454/) (2024)
- [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)
- [Graph convolutional networks enable fast hemorrhagic stroke monitoring with electrical impedance tomography](https://mlsanity.com/paper/2412.07888/) (2024)
- [SDEIT: Semantic-Driven Electrical Impedance Tomography](https://mlsanity.com/paper/2504.04185/) (2025)
- [Learned enclosure method for experimental EIT data](https://mlsanity.com/paper/2504.11512/) (2025)
- [Generative Prior-Guided Neural Interface Reconstruction for 3D Electrical Impedance Tomography](https://mlsanity.com/paper/2505.16487/) (2025)
- [QuantEIT: Ultra-Lightweight Quantum-Assisted Inference for Chest Electrical Impedance Tomography](https://mlsanity.com/paper/2507.14031/) (2025)
- [D2IP: Deep Dynamic Image Prior for 3D Time-sequence Pulmonary Impedance Imaging](https://mlsanity.com/paper/2507.14046/) (2025)
- [BREIT: A Framework for Brain Stroke Reconstruction using Multi-Frequency 3D EIT](https://mlsanity.com/paper/2606.28787/) (2026)

## Abstract (arXiv)

The mathematical problem for Electrical Impedance Tomography (EIT) is a highly nonlinear ill-posed inverse problem requiring carefully designed reconstruction procedures to ensure reliable image generation. D-bar methods are based on a rigorous mathematical analysis and provide robust direct reconstructions by using a low-pass filtering of the associated nonlinear Fourier data. Similarly to low-pass filtering of linear Fourier data, only using low frequencies in the image recovery process results in blurred images lacking sharp features such as clear organ boundaries. Convolutional Neural Networks provide a powerful framework for post-processing such convolved direct reconstructions. In this study, we demonstrate that these CNN techniques lead to sharp and reliable reconstructions even for the highly nonlinear inverse problem of EIT. The network is trained on data sets of simulated examples and then applied to experimental data without the need to perform an additional transfer training. Results for absolute EIT images are presented using experimental EIT data from the ACT4 and KIT4 EIT systems.