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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…

Numerical Analysis · Mathematics 2015-06-19 Sarah Hamilton , Juan Manuel Reyes , Samuli Siltanen , Xiaoqun Zhang

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…

Numerical Analysis · Mathematics 2018-05-09 Sarah Jane Hamilton , Andreas Hauptmann

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…

Numerical Analysis · Mathematics 2018-03-28 Sarah Hamilton , Andreas Hauptmann , Samuli Siltanen

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…

Numerical Analysis · Mathematics 2016-05-25 Sarah Jane Hamilton , Jennifer L. Mueller , Melody Alsaker

The first numerical implementation of a D-bar method in 3D using electrode data is presented. Results are compared to Calder\'on's method as well as more common TV and smoothness regularization-based methods. D-bar methods are based on…

Numerical Analysis · Mathematics 2020-07-08 Sarah J. Hamilton , David Isaacson , Ville Kolehmainen , Peter A. Muller , Jussi Toivanen , Patrick F. Bray

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…

Analysis of PDEs · Mathematics 2018-08-16 S. J. Hamilton , J. L. Mueller , T. R. Santos

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.…

Numerical Analysis · Mathematics 2014-04-25 Melody Dodd , Jennifer L. Mueller

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…

Image and Video Processing · Electrical Eng. & Systems 2025-08-11 Alexander Denker , Fabio Margotti , Jianfeng Ning , Kim Knudsen , Derick Nganyu Tanyu , Bangti Jin , Andreas Hauptmann , Peter Maass

Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs conductivity distributions within a body from boundary measurements. However, EIT reconstruction is hindered by its ill-posed nonlinear inverse…

Image and Video Processing · Electrical Eng. & Systems 2024-09-11 Bowen Tong , Junwu Wang , Dong Liu

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…

Numerical Analysis · Mathematics 2014-02-07 Sarah Jane Hamilton , Samuli Siltanen

Objective: To develop, and demonstrate the feasibility of, a novel image reconstruction method for absolute Electrical Impedance Tomography (a-EIT) that pairs deep learning techniques with real-time robust D-bar methods. Approach: A D-bar…

Numerical Analysis · Mathematics 2018-12-03 S. J. Hamilton , A. Hänninen , A. Hauptmann , V. Kolehmainen

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…

Analysis of PDEs · Mathematics 2015-06-25 Sarah Jane Hamilton , Matti Lassas , Samuli Siltanen

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…

Signal Processing · Electrical Eng. & Systems 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…

Numerical Analysis · Mathematics 2023-11-01 Siyu Cen , Bangti Jin , Kwancheol Shin , Zhi Zhou

Electrical Impedance Tomography (EIT) systems are becoming popular because they present several advantages over competing systems. However, EIT leads to images with very low resolution. Moreover, the nonuniform sampling characteristic of…

Computer Vision and Pattern Recognition · Computer Science 2019-05-01 Ricardo A. Borsoi , Julio C. C. Aya , Guilherme H. Costa , José C. M. Bermudez

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…

Numerical Analysis · Mathematics 2011-09-28 Samuli Siltanen , Janne P. Tamminen

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…

Machine Learning · Computer Science 2023-10-31 Derick Nganyu Tanyu , Jianfeng Ning , Andreas Hauptmann , Bangti Jin , Peter Maass

In this work, we develop an efficient high order discontinuous Galerkin (DG) method for solving the Electrical Impedance Tomography (EIT). EIT is a highly nonlinear ill-posed inverse problem where the interior conductivity of an object is…

Numerical Analysis · Mathematics 2023-06-01 Xiaosheng Li , Wei Wang

Electrical Impedance Tomography (EIT)-inspired tactile sensors are gaining attention in robotic tactile sensing due to their cost-effectiveness, safety, and scalability with sparse electrode configurations. This paper presents a data…

Robotics · Computer Science 2025-03-19 Huazhi Dong , Ronald B. Liu , Leo Micklem , Peisan Sharel E , Francesco Giorgio-Serchi , Yunjie Yang

Electrical Impedance Tomography (EIT) is a widely employed imaging technique in industrial inspection, geophysical prospecting, and medical imaging. However, the inherent nonlinearity and ill-posedness of EIT image reconstruction present…

Image and Video Processing · Electrical Eng. & Systems 2024-05-03 Huihui Wang , Guixian Xu , Qingping Zhou
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