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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

The aim of electrical impedance tomography is to reconstruct the admittivity distribution inside a physical body from boundary measurements of current and voltage. Due to the severe ill-posedness of the underlying inverse problem, the…

Analysis of PDEs · Mathematics 2022-07-19 Jérémi Dardé , Nuutti Hyvönen , Aku Seppänen , Stratos Staboulis

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

This work considers using reduced basis techniques in connection to (smoothened) total variation regularization in electrical impedance tomography, but analogous ideas can also be used for other inverse elliptic boundary value problems. It…

Numerical Analysis · Mathematics 2026-02-18 A. Hannukainen , N. Hyvönen , V. Toresen

The regularized D-bar method is a popular method for solving Electrical Impedance Tomography (EIT) problems due to its efficiency and simplicity. It utilizes the low-pass truncated scattering data in the non-linear Fourier domain to solve…

Numerical Analysis · Mathematics 2025-02-10 Xiang Cao , Qiaoqiao Ding , Xiaoqun Zhang

Objective: Absolute images have important applications in medical Electrical Impedance Tomography (EIT) imaging, but the traditional minimization and statistical based computations are very sensitive to modeling errors and noise. In this…

Analysis of PDEs · Mathematics 2018-08-16 S. J. Hamilton , J. L. Mueller , T. R. Santos

This paper presents an iterative inversion algorithm for computed tomography image reconstruction that performs well in terms of accuracy and speed using limited data. The computational method combines an image domain technique and…

Image and Video Processing · Electrical Eng. & Systems 2019-01-17 Victor Churchill , Anne Gelb

This paper deals with the problem of building fast and reliable 3D reconstruction methods for blood flows for which partial information is given by Doppler ultrasound measurements. This task is of interest in medicine since it could enrich…

Numerical Analysis · Mathematics 2020-11-05 Felipe Galarce , Jean-Frédéric Gerbeau , Damiano Lombardi , Olga Mula

We propose three fast algorithms for solving the inverse problem of the thermoacoustic tomography corresponding to certain acquisition geometries. Two of these methods are designed to process the measurements done with point-like detectors…

Analysis of PDEs · Mathematics 2011-02-08 Leonid Kunyansky

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

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

Electrical Impedance Tomography (EIT) systems are becoming popular because they present several advantages over competing systems. However, EIT leads to images with very low resolution. Moreover, the nonuniform sampling characteristic of…

Computer Vision and Pattern Recognition · Computer Science 2019-05-01 Ricardo A. Borsoi , Julio C. C. Aya , Guilherme H. Costa , José C. M. Bermudez

We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the…

Analysis of PDEs · Mathematics 2015-05-20 Peter Kuchment , Leonid Kunyansky

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

A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned…

Machine Learning · Computer Science 2023-03-07 Ruchi Guo , Shuhao Cao , Long Chen

This paper discusses the reconstruction of partially sampled spectrum-images to accelerate the acquisition in scanning transmission electron microscopy (STEM). The problem of image reconstruction has been widely considered in the literature…

Image and Video Processing · Electrical Eng. & Systems 2020-02-05 Etienne Monier , Thomas Oberlin , Nathalie Brun , Xiaoyan Li , Marcel Tencé , Nicolas Dobigeon

We show how to eliminate the error caused by an incorrectly modeled boundary in electrical impedance tomography (EIT). In practical measurements, one usually lacks the exact knowledge of the boundary. Because of this the numerical…

Analysis of PDEs · Mathematics 2007-05-23 Ville Kolehmainen , Matti Lassas , Petri Ola

In this paper, we present a discussion on the algorithms design of Electrical Impedance Tomography (EIT) for biomedical applications. Based on the Maxwell differential equations and the derived the finite element(FE) linear equations, we…

Signal Processing · Electrical Eng. & Systems 2019-01-23 Mingyong Zhou , Hongyu Zhu

Electrical impedance tomography (EIT) is a non-invasive imaging technique, capable of reconstructing images of the electrical conductivity of tissues and materials. It is popular in diverse application areas, from medical imaging to…

Computer Vision and Pattern Recognition · Computer Science 2024-12-24 Shuaikai Shi , Ruiyuan Kang , Panos Liatsis

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