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Electrical impedance tomography (EIT) is an imaging modality in which the conductivity distribution inside a target is reconstructed based on voltage measurements from the surface of the target. Reconstructing the conductivity distribution…

Mathematical Physics · Physics 2012-07-05 Antti Lipponen , Aku Seppänen , Jari Kaipio

In this paper, we consider an inverse conductivity problem on a bounded domain $\Omega\subset\mathbb{R}^n$, $n\geq2$, also known as Electrical Impedance Tomography (EIT), for the case where unknown impenetrable obstacles are embedded into…

Analysis of PDEs · Mathematics 2021-04-29 Jiaqing Yang

The aim of Electrical Impedance Tomography (EIT) is to determine the electrical conductivity distribution inside a domain by applying currents and measuring voltages on its boundary. Mathematically, the EIT reconstruction task can be…

Numerical Analysis · Mathematics 2024-05-07 Monica Pragliola , Daniela Calvetti , Erkki Somersalo

Electrical Impedance Tomography (EIT) is a non-invasive medical imaging method that reconstructs electrical conductivity mediums from boundary voltage-current measurements, but its severe ill-posedness renders direct operator learning with…

Numerical Analysis · Mathematics 2026-01-14 Amit Bhat , Ke Chen , Chunmei Wang

In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to…

Analysis of PDEs · Mathematics 2018-03-20 Elena Beretta , Stefano Micheletti , Simona Perotto , Matteo Santacesaria

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

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) plays a crucial role in non-invasive imaging, with both medical and industrial applications. In this paper, we present three data-driven reconstruction methods for EIT imaging. These three approaches…

Image and Video Processing · Electrical Eng. & Systems 2024-07-03 Alexander Denker , Zeljko Kereta , Imraj Singh , Tom Freudenberg , Tobias Kluth , Peter Maass , Simon Arridge

Electrical impedance tomography (EIT) is a novel computational imaging technology. In order to improve the quality and spatial resolution of the reconstructed images, the G-CNN and HG-CNN algorithms are proposed based on a one-dimensional…

This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a…

Analysis of PDEs · Mathematics 2025-12-08 Henrik Garde

This work presents a new constructive uniqueness proof for Calder\'on's inverse problem of electrical impedance tomography, subject to local Cauchy data, for a large class of piecewise constant conductivities that we call "piecewise…

Analysis of PDEs · Mathematics 2020-08-18 Henrik Garde

We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain $\Omega\subset\mathbb{R}^n$ and we show that a…

Analysis of PDEs · Mathematics 2016-11-03 Giovanni Alessandrini , Maarten V. de Hoop , Romina Gaburro , Eva Sincich

Electrical impedance tomography is an imaging modality for extracting information on the conductivity distribution inside a physical body from boundary measurements of current and voltage. In many practical applications, it is a priori…

Numerical Analysis · Mathematics 2014-06-06 Lauri Harhanen , Nuutti Hyvönen , Helle Majander , Stratos Staboulis

We introduce a new geometric approach for the homogenization and inverse homogenization of the divergence form elliptic operator with rough conductivity coefficients $\sigma(x)$ in dimension two. We show that conductivity coefficients are…

Analysis of PDEs · Mathematics 2009-05-13 Mathieu Desbrun , Roger D. Donaldson , Houman Owhadi

This short note considerably simplifies a reconstruction method by the author (Comm. PDE, 45(9):1118--1133, 2020), for reconstructing piecewise constant layered conductivities (PCLC) from partial boundary measurements in electrical…

Analysis of PDEs · Mathematics 2022-08-24 Henrik Garde

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 paper aims to numerically solve the two-dimensional electrical impedance tomography (EIT) with Cauchy data. This inverse problem is highly challenging due to its severe ill-posed nature and strong nonlinearity, which necessitates…

Numerical Analysis · Mathematics 2025-07-22 Kai Li , 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

Parallel-beam X-ray computed tomography (CT) and electrical impedance tomography (EIT) are two imaging modalities which stem from completely different underlying physics, and for decades have been thought to have little in common either…

Electrical Impedance Tomography (EIT) is a noninvasive imaging technique that does not use ionizing radiation, with application both in environmental sciences and in health. Image reconstruction is performed by solving an inverse problem…