English
Related papers

Related papers: Inverse conductivity problem with an imperfectly k…

200 papers

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

We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced…

Mathematical Physics · Physics 2009-11-10 S. Ciulli , M. K. Pidcock , C. Sebu

Electrical impedance tomography is an imaging modality for extracting information on the interior structure of a physical body from boundary measurements of current and voltage. This work studies a new robust way of modeling the contact…

Numerical Analysis · Mathematics 2022-07-06 J. Dardé , N. Hyvönen , T. Kuutela , T. Valkonen

In electrical impedance tomography the electrical conductivity inside a physical body is computed from electro-static boundary measurements. The focus of this paper is to extend recent result for the 2D problem to 3D. Prior information…

Numerical Analysis · Mathematics 2016-01-20 Henrik Garde , Kim Knudsen

We study the local recovery of an unknown piecewise constant anisotropic conductivity in EIT (electric impedance tomography) on certain bounded Lipschitz domains $\Omega$ in $\mathbb{R}^2$ with corners. The measurement is conducted on a…

Analysis of PDEs · Mathematics 2023-02-01 Maarten V. de Hoop , Takashi Furuya , Ching-Lung Lin , Gen Nakamura , Manmohan Vashisth

A direct three dimensional EIT reconstruction algorithm based on complex geometrical optics solutions and a nonlinear scattering transform is presented and implemented for spherically symmetric conductivity distributions. The scattering…

Analysis of PDEs · Mathematics 2010-03-22 Jutta Bikowski , Kim Knudsen , Jennifer Mueller

We propose an immersed boundary scheme for the numerical resolution of the Complete Electrode Model in Electrical Impedance Tomography, that we use as a main ingredient in the resolution of inverse problems in medical imaging. Such method…

Numerical Analysis · Mathematics 2023-05-24 Jérémi Dardé , Niami Nasr , Lisl Weynans

The reconstruction problem in electrical impedance tomography is highly ill-posed, and it is often observed numerically that reconstructions have poor resolution far away from the measurement boundary but better resolution near the…

Analysis of PDEs · Mathematics 2017-05-23 Henrik Garde , Kim Knudsen

This work implements and numerically tests the direct reconstruction algorithm introduced in [Garde & Hyv\"onen, SIAM J. Math. Anal., 2024] for two-dimensional linearized electrical impedance tomography. Although the algorithm was…

Numerical Analysis · Mathematics 2026-02-18 Antti Autio , Henrik Garde , Markus Hirvensalo , Nuutti Hyvönen

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

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

We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality Ultrasound Modulated…

Numerical Analysis · Mathematics 2018-06-13 François Monard , Donsub Rim

In this article, we consider the problem of finding the support of an inhomogenous possibly anisotropic inclusion in a background of constant electric conductivity from the electrical impedance tomography data at the boundary of a bounded…

Functional Analysis · Mathematics 2007-05-23 Erkki J. Somersalo

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

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

We review developments, issues and challenges in Electrical Impedance Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT, Manchester 2003. We focus on the necessity for three dimensional data collection and…

Medical Physics · Physics 2008-07-31 William R. B. Lionheart

An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…

Optimization and Control · Mathematics 2022-09-27 Paul R. Arbic , Vladislav Bukshtynov

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…

Optimization and Control · Mathematics 2018-08-29 B. J. Adesokan , Kim Knudsen , Venkateswaran P. Krishnan , Souvik Roy

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

Novel reconstruction methods for electrical impedance tomography (EIT) often require voltage measurements on current-driven electrodes. Such measurements are notoriously difficult to obtain in practice as they tend to be affected by unknown…

Numerical Analysis · Mathematics 2018-10-11 Bastian Harrach