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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…

数值分析 · 数学 2018-05-09 Sarah Jane Hamilton , Andreas Hauptmann

The regularized D-bar method is a popular method for solving Electrical Impedance Tomography (EIT) problems due to its efficiency and simplicity. It utilizes the low-pass truncated scattering data in the non-linear Fourier domain to solve…

数值分析 · 数学 2025-02-10 Xiang Cao , Qiaoqiao Ding , Xiaoqun Zhang

In Electrical Impedance Tomography (EIT), the internal conductivity of a body is recovered via current and voltage measurements taken at its surface. The reconstruction task is a highly ill-posed nonlinear inverse problem, which is very…

数值分析 · 数学 2018-03-28 Sarah Hamilton , Andreas Hauptmann , Samuli Siltanen

Objective: Absolute images have important applications in medical Electrical Impedance Tomography (EIT) imaging, but the traditional minimization and statistical based computations are very sensitive to modeling errors and noise. In this…

偏微分方程分析 · 数学 2018-08-16 S. J. Hamilton , J. L. Mueller , T. R. Santos

Electrical impedance tomography (EIT) is a non-invasive imaging method in which an unknown physical body is probed with electric currents applied on the boundary, and the internal conductivity distribution is recovered from the measured…

数值分析 · 数学 2014-02-07 Sarah Jane Hamilton , Samuli Siltanen

Electrical Impedance Tomography (EIT) is a powerful imaging modality widely used in medical diagnostics, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity distribution of…

图像与视频处理 · 电气工程与系统科学 2025-08-11 Alexander Denker , Fabio Margotti , Jianfeng Ning , Kim Knudsen , Derick Nganyu Tanyu , Bangti Jin , Andreas Hauptmann , Peter Maass

Deep learning has been widely employed to solve the Electrical Impedance Tomography (EIT) image reconstruction problem. Most existing physical model-based and learning-based approaches focus on 2D EIT image reconstruction. However, when…

图像与视频处理 · 电气工程与系统科学 2022-09-01 Zhaoguang Yi , Zhou Chen , Yunjie Yang

Objective: The strengths of Electrical Impedance Tomography (EIT) are its capability of imaging the internal body by using a noninvasive, radiation safe technique, and the absence of known hazards. In this paper we introduce a novel idea of…

信号处理 · 电气工程与系统科学 2022-03-08 Sebastien Martin

Electrical impedance tomography (EIT) is a noninvasive medical imaging modality utilizing the current-density/voltage data measured on the surface of the subject. Calder\'on's method is a relatively recent EIT imaging algorithm that is…

数值分析 · 数学 2023-11-01 Siyu Cen , Bangti Jin , Kwancheol Shin , Zhi Zhou

The Regularized D-bar method for Electrical Impedance Tomography provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e. without iterations. It is based on a low-pass filtering in the…

数值分析 · 数学 2015-06-19 Sarah Hamilton , Juan Manuel Reyes , Samuli Siltanen , Xiaoqun Zhang

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…

机器学习 · 计算机科学 2023-10-31 Derick Nganyu Tanyu , Jianfeng Ning , Andreas Hauptmann , Bangti Jin , Peter Maass

Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely…

数值分析 · 数学 2016-05-25 Sarah Jane Hamilton , Jennifer L. Mueller , Melody Alsaker

A novel computational, non-iterative and noise-robust reconstruction method is introduced for the planar anisotropic inverse conductivity problem. The method is based on bypassing the unstable step of the reconstruction of the values of the…

偏微分方程分析 · 数学 2015-06-25 Sarah Jane Hamilton , Matti Lassas , Samuli Siltanen

The aim of this paper is to show the feasibility of the D-bar method for real-time 2-D EIT reconstructions. A fast implementation of the D-bar method for reconstructing conductivity changes on a 2-D chest-shaped domain is described.…

数值分析 · 数学 2014-04-25 Melody Dodd , Jennifer L. Mueller

The aim of electrical impedance tomography is to form an image of the conductivity distribution inside an unknown body using electric boundary measurements. The computation of the image from measurement data is a non-linear ill-posed…

数值分析 · 数学 2011-09-28 Samuli Siltanen , Janne P. Tamminen

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.…

计算物理 · 物理学 2020-01-29 Yuwei Fan , Lexing Ying

Electrical impedance tomography (EIT) is a non-invasive imaging technique, capable of reconstructing images of the electrical conductivity of tissues and materials. It is popular in diverse application areas, from medical imaging to…

计算机视觉与模式识别 · 计算机科学 2024-12-24 Shuaikai Shi , Ruiyuan Kang , Panos Liatsis

Electrical impedance tomography (EIT) is a non-invasive functional imaging technology. In order to enhance the quality of lung EIT images, novel algorithms, namely LSTM-LSTM, LSTM-BiLSTM, BiLSTM-LSTM, and BiLSTM-BiLSTM, leveraging LSTM or…

生物物理 · 物理学 2025-04-22 Zhenzhong Song , Jianping Li , Jun Zhang , Hanyun Wen , Suqin Zhang , Wei Jiang , Xingxing Zhou

The objective of electrical impedance tomography (EIT) is to reconstruct the internal conductivity of a physical body based on current and voltage measurements at the boundary of the body. In many medical applications the exact shape of the…

最优化与控制 · 数学 2021-10-25 J. P. Agnelli , V. Kolehmainen , M. Lassas , P. Ola , S. Siltanen

Electrical Impedance Tomography (EIT) is a promising noninvasive imaging technique that reconstructs the spatial conductivity distribution from boundary voltage measurements. However, it poses a highly nonlinear and ill-posed inverse…

信号处理 · 电气工程与系统科学 2025-12-16 Xuanxuan Yang , Yangming Zhang , Haofeng Chen , Gang Ma , Xiaojie Wang
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