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Two reconstruction methods of Electrical Impedance Tomography (EIT) are numerically compared for nonsmooth conductivities in the plane based on the use of complex geometrical optics (CGO) solutions to D-bar equations involving the global…

Analysis of PDEs · Mathematics 2015-06-17 Kari Astala , Lassi Päivärinta , Juan Manuel Reyes , Samuli Siltanen

A direct reconstruction algorithm for complex conductivities in $W^{2,\infty}(\Omega)$, where $\Omega$ is a bounded, simply connected Lipschitz domain in $\mathbb{R}^2$, is presented. The framework is based on the uniqueness proof by…

Analysis of PDEs · Mathematics 2012-11-13 S. J. Hamilton , C. N. L. Herrera , J. L. Mueller , A. Von Herrmann

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

This paper considers the problem of noise-robust neural operator approximation for the solution map of Calder\'on's inverse conductivity problem. In this continuum model of electrical impedance tomography (EIT), the boundary measurements…

Numerical Analysis · Mathematics 2025-11-26 Maarten V. de Hoop , Nikola B. Kovachki , Matti Lassas , Nicholas H. Nelsen

Current-voltage measurements in electrical impedance tomography can be partially ordered with respect to definiteness of the associated self-adjoint Neumann-to-Dirichlet operators (NtD). With this ordering, a point-wise larger conductivity…

Numerical Analysis · Mathematics 2018-12-14 Bastian Harrach , Marcel Ullrich

This work introduces a computational framework for applying absolute electrical impedance tomography to head imaging without accurate information on the head shape or the electrode positions. A library of fifty heads is employed to build a…

Numerical Analysis · Mathematics 2019-02-18 Valentina Candiani , Antti Hannukainen , Nuutti Hyvönen

We present a procedure for recovering the conformal factor of an anisotropic conductivity matrix in a known conformal class in a domain in Euclidean space of dimension greater than or equal to 2. The method requires one internal…

Analysis of PDEs · Mathematics 2013-03-01 Nicholas Hoell , Amir Moradifam , Adrian Nachman

Physics has played a fundamental role in medicine sciences, specially in imaging diagnostic. Currently, image reconstruction techniques are already taught in Physics courses and there is a growing interest in new potential applications. The…

Physics Education · Physics 2013-02-22 Olavo Henrique Menin , Vanessa Rolnik , Alexandre Souto Martinez

We study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution $\gamma$ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction…

Functional Analysis · Mathematics 2007-05-23 Kim Knudsen , Alexandru Tamasan

In this paper, we will discuss the use of a Sampling Method to reconstruct impenetrable inclusions from Electrostatic Cauchy data. We consider the case of a perfectly conducting and impedance inclusion. In either case, we show that the…

Analysis of PDEs · Mathematics 2021-02-10 Isaac Harris

Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions,…

Numerical Analysis · Mathematics 2018-08-16 Henrik Garde

A new non-linear optimization approach is proposed for the sparse reconstruction of log-conductivities in current density impedance imaging. This framework comprises of minimizing an objective functional involving a least squares fit of the…

Optimization and Control · Mathematics 2020-06-30 Madhu Gupta , Rohit Kumar Mishra , Souvik Roy

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

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

The D-bar method at negative energy is numerically implemented. Using the method we are able to numerically reconstruct potentials and investigate exceptional points at negative energy. Subsequently, applying the method to Diffusive Optical…

Numerical Analysis · Mathematics 2016-02-03 Janne P. Tamminen , Tanja Tarvainen , Samuli Siltanen

The Electrical Resistance Tomography (ERT) technique is applied to the measurement of sheet conductance maps of both uniform and patterned conductive thin films. Images of the sheet conductance spatial distribution, and local conductivity…

Instrumentation and Detectors · Physics 2016-06-21 Alessandro Cultrera , Luca Callegaro

We consider the two-dimensional version of Calder\`on's problem. When the D-N map is assumed to be known up to an error level $\varepsilon_0$, we investigate how the resolution in the determination of the unknown conductivity deteriorates…

Analysis of PDEs · Mathematics 2018-01-16 Giovanni Alessandrini , Andrea Scapin

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…

Geophysics · Physics 2012-05-29 Nick Polydorides , Alireza Aghasi , Eric L. Miller

A path integral Monte Carlo method (PIMC) based on Feynman-Kac formula for mixed boundary conditions of elliptic equations is proposed to solve the forward problem of electrical impedance tomography (EIT) on the boundary to obtain…

Numerical Analysis · Mathematics 2019-08-01 Yijing Zhou , Wei Cai

Perturbative expansions in physical applications are generically divergent, and their physical content can be studied using Borel analysis. Given just a finite number of terms of such an expansion, this input data can be analyzed in…

High Energy Physics - Theory · Physics 2021-10-22 Ovidiu Costin , Gerald V. Dunne