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Deep learning has been widely employed to solve the Electrical Impedance Tomography (EIT) image reconstruction problem. Most existing physical model-based and learning-based approaches focus on 2D EIT image reconstruction. However, when…

Image and Video Processing · Electrical Eng. & Systems 2022-09-01 Zhaoguang Yi , Zhou Chen , Yunjie Yang

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

Electrical impedance tomography (EIT) is a non-invasive imaging technique, which has been widely used in the fields of industrial inspection, medical monitoring and tactile sensing. However, due to the inherent non-linearity and…

Computer Vision and Pattern Recognition · Computer Science 2025-01-13 Duanpeng Shi , Wendong Zheng , Di Guo , Huaping Liu

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

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

For electrical impedance tomography (EIT), most practical reconstruction methods are based on linearizing the underlying non-linear inverse problem. Recently, it has been shown that the linearized problem still contains the exact shape…

Numerical Analysis · Mathematics 2018-11-20 Moon Kyung Choi , Bastian Harrach , Jin Keun Seo

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

Inverse problems often involve matching observational data using a physical model that takes a large number of parameters as input. These problems tend to be under-constrained and require regularization to impose additional structure on the…

Computational Physics · Physics 2019-06-07 Daniel O'Malley , John K. Golden , Velimir V. Vesselinov

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

Computer Vision and Pattern Recognition · Computer Science 2020-06-17 Erich Kobler , Alexander Effland , Karl Kunisch , Thomas Pock

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 majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method…

Image and Video Processing · Electrical Eng. & Systems 2021-07-12 William Herzberg , Daniel B. Rowe , Andreas Hauptmann , Sarah J. Hamilton

In this paper we investigate the problem of identifying conductivity in electrical impedance tomography from one boundary measurement. A variational method with total variation regularization is here proposed to tackle this problem. We…

Analysis of PDEs · Mathematics 2017-09-26 Michael Hinze , Barbara Kaltenbacher , Tran Nhan Tam Quyen

Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…

Optimization and Control · Mathematics 2020-02-19 Erich Kobler , Alexander Effland , Karl Kunisch , Thomas Pock

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

We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…

Optimization and Control · Mathematics 2021-01-27 S. Kindermann , A. Leitao

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 present a study of the numerical solution of the two dimensional electrical impedance tomography problem, with noisy measurements of the Dirichlet to Neumann map. The inversion uses parametrizations of the conductivity on optimal grids.…

Mathematical Physics · Physics 2015-06-03 Liliana Borcea , Fernando Guevara Vasquez , Alexander V. Mamonov

Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Their handy size makes these tools very practical…

Numerical Analysis · Mathematics 2021-09-21 Gian Piero Deidda , Patricia Diaz de Alba , Giuseppe Rodriguez , Giulio Vignoli

Objective: This paper investigates how generative models, trained on ground-truth images, can be used \changes{as} priors for inverse problems, penalizing reconstructions far from images the generator can produce. The aim is that learned…

Image and Video Processing · Electrical Eng. & Systems 2023-08-07 Margaret Duff , Ivor J. A. Simpson , Matthias J. Ehrhardt , Neill D. F. Campbell

A new iterative image reconstruction algorithm for electrical capacitance tomography (ECT) is proposed that is based on iterative soft thresholding of a total variation penalty and adaptive reweighted compressive sensing. This algorithm…

Computer Vision and Pattern Recognition · Computer Science 2016-11-22 Kezhi Li , Daniel Holland