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This work considers finding optimal positions for the electrodes within the Bayesian paradigm based on available prior information on the conductivity; the aim is to place the electrodes so that the posterior density of the (discretized)…

Optimization and Control · Mathematics 2014-09-11 Nuutti Hyvönen , Aku Seppänen , Stratos Staboulis

In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…

Numerical Analysis · Mathematics 2017-04-10 Andreas Hauptmann , Matteo Santacesaria , Samuli Siltanen

This work introduces a method for preprocessing measurements of electrical impedance tomography to considerably reduce the effect uncertainties in the electrode contacts have on the reconstruction quality, without a need to explicitly…

Numerical Analysis · Mathematics 2024-12-20 Altti Jääskeläinen , Jussi Toivanen , Asko Hänninen , Ville Kolehmainen , Nuutti Hyvönen

We explain how to build invisible isotropic conductivity perturbations of the unit conductivity in the framework of the point electrode model for two-dimensional electrical impedance tomography. The theoretical approach, based on solving a…

Analysis of PDEs · Mathematics 2014-12-23 Lucas Chesnel , Nuutti Hyvönen , Stratos Staboulis

In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…

Numerical Analysis · Mathematics 2019-05-16 Bangti Jin , Yifeng Xu , Jun Zou

The first partial boundary data complex geometrical optics based methods for electrical impedance tomography in three dimensions are developed, and tested, on simulated and experimental data. The methods provide good localization of targets…

Medical Physics · Physics 2024-12-17 Sarah J. Hamilton , Peter Muller , Ville Kolehmainen , Jussi Toivanen

We develop a boundary integral equation-based numerical method to solve for the electrostatic potential in two dimensions, inside a medium with piecewise constant conductivity, where the boundary condition is given by the complete electrode…

Numerical Analysis · Mathematics 2024-03-28 Teemu Tyni , Adam R Stinchcombe , Spyros Alexakis

Electrical Impedance Tomography can be cost-effective, portable, non-invasive imaging technique. It has preclinical and a few of them already proven industrial applications. This technique can only recover images of low spatial and contrast…

Instrumentation and Detectors · Physics 2023-04-17 Vaishali Sharma , Mayank Goswami

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

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

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

In electrical impedance tomography, we aim to solve the conductivity within a target body through electrical measurements made on the surface of the target. This inverse conductivity problem is severely ill-posed, especially in real…

Optimization and Control · Mathematics 2022-05-24 Jyrki Jauhiainen , Aku Seppänen , Tuomo Valkonen

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

This work considers the optimization of electrode positions in head imaging by electrical impedance tomography. The study is motivated by maximizing the sensitivity of electrode measurements to conductivity changes when monitoring the…

Numerical Analysis · Mathematics 2023-12-19 N. Hyvönen , A. Jääskeläinen , R. Maity , A. Vavilov

Electron tomography is a technique used in both materials science and structural biology to image features well below optical resolution limit. In this work, we present a new algorithm for reconstructing the three-dimensional(3D)…

Signal Processing · Electrical Eng. & Systems 2018-07-12 David Ren , Michael Chen , Laura Waller , Colin Ophus

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

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

Electrical impedance tomography (EIT) uses current-voltage measurements on the surface of an imaging subject to detect conductivity changes or anomalies. EIT is a promising new technique with great potential in medical imaging and…

Numerical Analysis · Mathematics 2018-11-19 Bastian Harrach , Marcel Ullrich

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 provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…

Numerical Analysis · Mathematics 2016-10-06 Giovanni S. Alberti , Habib Ammari , Bangti Jin , Jin-Keun Seo , Wenlong Zhang