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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 noninvasive imaging modality that allows a continuous assessment of changes in regional bioimpedance of different organs. One of its most common biomedical applications is monitoring regional…

Image and Video Processing · Electrical Eng. & Systems 2020-10-20 Nils Strodthoff , Claas Strodthoff , Tobias Becher , Norbert Weiler , Inéz Frerichs

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

Electron tomography is a widely used experimental technique for analyzing nanometer-scale structures of a large variety of materials in three dimensions. Unfortunately, the acquisition of conventional electron tomography tilt series can…

Materials Science · Physics 2020-10-01 Hans Vanrompay , Alexander Skorikov , Eva Bladt , Armand Béché , Bert Freitag , Jo Verbeeck , Sara Bals

Electron tomography, as an important 3D imaging method, offers a powerful method to probe the 3D structure of materials from the nano- to the atomic-scale. However, as a grant challenge, radiation intolerance of the nanoscale samples and…

Materials Science · Physics 2020-03-30 Chunyang Wang , Guanglei Ding , Yitong Liu , Huolin L. Xin

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

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

Magnetic resonance imaging (MRI) based electrical properties tomography (EPT) is the quantification of the conductivity and permittivity of different tissues. These electrical properties can be obtained through different reconstruction…

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

Electrical Impedance Tomography (EIT) provides a non-invasive, portable imaging modality with significant potential in medical and industrial applications. Despite its advantages, EIT encounters two primary challenges: the ill-posed nature…

Image and Video Processing · Electrical Eng. & Systems 2025-04-29 Chuyu Wang , Huiting Deng , Dong Liu

Full 3D inversion of time-domain Airborne ElectroMagnetic (AEM) data requires specialists' expertise and a tremendous amount of computational resources, not readily available to everyone. Consequently, quasi-2D/3D inversion methods are…

Geophysics · Physics 2022-11-18 Wouter Deleersnyder , David Dudal , Thomas Hermans

We are aiming to identify the thin insulating inhomogeneities and small conductive inhomogeneities inside an electrically conducting medium by using multi-frequency electrical impedance tomography (mfEIT). The thin insulating…

Analysis of PDEs · Mathematics 2016-08-24 Habib Ammari , Jin Keun Seo , Tingting Zhang

The inverse problem in Acousto-Electric tomography concerns the reconstruction of the electric conductivity in a domain from knowledge of the power density function in the interior of the body. This interior power density results from…

Numerical Analysis · Mathematics 2020-01-09 Changyou Li , Mirza Karamehmedovic , Ekaterina Sherina , Kim Knudsen

The aim of this paper is to propose an optimal control optimization algorithm for reconstructing admittivity distributions (i.e., both conductivity and permittivity) from multi-frequency micro-electrical impedance tomography. A convergent…

Analysis of PDEs · Mathematics 2014-03-25 Habib Ammari , Laure Giovangigli , Loc Hoang Nguyen , Jin-Keun Seo

Consider an inverse problem of the simultaneous recovery of boundary impedance and internal conductivity in the electrical impedance tomography (EIT) model using local internal measurement data, which is governed by a boundary value problem…

Analysis of PDEs · Mathematics 2025-09-22 Jinchao Pan , Jijun Liu

Radon Transformation is generally used to construct optical image (like CT image) from the projection data in biomedical imaging. In this paper, the concept of Radon Transformation is implemented to reconstruct Electrical Impedance…

Computer Vision and Pattern Recognition · Computer Science 2012-11-07 Md. Ali Hossain , Ahsan-Ul-Ambia , Md. Aktaruzzaman , Md. Ahaduzzaman Khan

The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…

Analysis of PDEs · Mathematics 2015-06-11 Ok Kyun Lee , Hyeonbae Kang , Jong Chul Ye , Mikyoung Lim

Electrochemical Impedance Spectroscopy (EIS) is a non-invasive technique widely used for understanding charge transfer and charge transport processes in electrochemical systems and devices. Standard approaches for the interpretation of EIS…

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

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…

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