# Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approaches

arXiv: https://arxiv.org/abs/2310.18636 · HTML: https://mlsanity.com/paper/2310.18636/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 109 references that are in the map.
- First posted on arXiv 28 Oct 2023.

## Builds on (most cited first, 22 of 22)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Wavelet neural operator: a neural operator for parametric partial differential equations](https://mlsanity.com/paper/2205.02191/) (2022)
- [Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems](https://mlsanity.com/paper/2212.03130/) (2022)
- [Numerical Solution of Inverse Problems by Weak Adversarial Networks](https://mlsanity.com/paper/2002.11340/) (2020)
- [Deep D-bar: Real time Electrical Impedance Tomography Imaging with Deep Neural Networks](https://mlsanity.com/paper/1711.03180/) (2017)
- [Transformer Meets Boundary Value Inverse Problems](https://mlsanity.com/paper/2209.14977/) (2022)
- [Solving Electrical Impedance Tomography with Deep Learning](https://mlsanity.com/paper/1906.03944/) (2019)
- [Beltrami-Net: Domain Independent Deep D-bar Learning for Absolute Imaging with Electrical Impedance Tomography (a-EIT)](https://mlsanity.com/paper/1811.12830/) (2018)
- [Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems](https://mlsanity.com/paper/2103.15138/) (2021)
- [MMV-Net: A Multiple Measurement Vector Network for Multi-frequency Electrical Impedance Tomography](https://mlsanity.com/paper/2105.12474/) (2021)
- [An efficient Quasi-Newton method for nonlinear inverse problems via learned singular values](https://mlsanity.com/paper/2012.07676/) (2020)
- [A Direct Sampling-Based Deep Learning Approach for Inverse Medium Scattering Problems](https://mlsanity.com/paper/2305.00250/) (2023)
- [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 Convergent Adaptive Finite Element Method for Electrical Impedance Tomography](https://mlsanity.com/paper/1608.03170/) (2016)
- [Adaptive Reconstruction for Electrical Impedance Tomography with a Piecewise Constant Conductivity](https://mlsanity.com/paper/1904.08837/) (2019)

## Built on by (most cited first, 2 of 2)

- [Graph convolutional networks enable fast hemorrhagic stroke monitoring with electrical impedance tomography](https://mlsanity.com/paper/2412.07888/) (2024)
- [Learned enclosure method for experimental EIT data](https://mlsanity.com/paper/2504.11512/) (2025)

## Abstract (arXiv)

Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity distribution of an object from measurements taken on its boundary. It is severely ill-posed, necessitating advanced computational methods for accurate image reconstructions. Recent years have witnessed significant progress, driven by innovations in analytic-based approaches and deep learning. This review explores techniques for solving the EIT inverse problem, focusing on the interplay between contemporary deep learning-based strategies and classical analytic-based methods. Four state-of-the-art deep learning algorithms are rigorously examined, harnessing the representational capabilities of deep neural networks to reconstruct intricate conductivity distributions. In parallel, two analytic-based methods, rooted in mathematical formulations and regularisation techniques, are dissected for their strengths and limitations. These methodologies are evaluated through various numerical experiments, encompassing diverse scenarios that reflect real-world complexities. A suite of performance metrics is employed to assess the efficacy of these methods. These metrics collectively provide a nuanced understanding of the methods' ability to capture essential features and delineate complex conductivity patterns. One novel feature of the study is the incorporation of variable conductivity scenarios, introducing a level of heterogeneity that mimics textured inclusions. This departure from uniform conductivity assumptions mimics realistic scenarios where tissues or materials exhibit spatially varying electrical properties. Exploring how each method responds to such variable conductivity scenarios opens avenues for understanding their robustness and adaptability.