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This paper is devoted to proving convergence rates of variational and iterative regularization methods under variational source conditions VSCs for inverse problems whose linearization satisfies a range invariance condition. In order to…

Numerical Analysis · Mathematics 2024-03-28 Barbara Kaltenbacher

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

Multi-frequency Electrical Impedance Tomography (mfEIT) is a promising biomedical imaging technique that estimates tissue conductivities across different frequencies. Current state-of-the-art (SOTA) algorithms, which rely on supervised…

Image and Video Processing · Electrical Eng. & Systems 2024-09-18 Hao Fang , Zhe Liu , Yi Feng , Zhen Qiu , Pierre Bagnaninchi , Yunjie Yang

Multi-frequency Electrical Impedance Tomography (mfEIT) is an emerging biomedical imaging modality to reveal frequency-dependent conductivity distributions in biomedical applications. Conventional model-based image reconstruction methods…

Image and Video Processing · Electrical Eng. & Systems 2021-05-27 Zhou Chen , Jinxi Xiang , Pierre Bagnaninchi , Yunjie Yang

Time-lapse electrical resistivity tomography (ERT) is a popular geophysical method to estimate three-dimensional (3D) permeability fields from electrical potential difference measurements. Traditional inversion and data assimilation methods…

Geophysics · Physics 2022-08-10 M. K. Mudunuru , E. L. D. Cromwell , H. Wang , X. Chen

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

To study the fundamental physics of complex multiphase flow systems using advanced measurement techniques, especially the electrical capacitance tomography (ECT) approach, this article carries out an initial literature review of the ECT…

Computer Vision and Pattern Recognition · Computer Science 2015-10-16 Kezhi Li

Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse…

Computational Physics · Physics 2021-12-15 Meghdoot Mozumder , Andreas Hauptmann , Ilkka Nissilä , Simon R. Arridge , Tanja Tarvainen

We study the Electrical Impedance Tomography Bayesian inverse problem for recovering the conductivity given noisy measurements of the voltage on some boundary surface electrodes. The uncertain conductivity depends linearly on a countable…

Numerical Analysis · Mathematics 2023-06-16 Quang Huy Pham , Viet Ha Hoang

Electrical impedance tomography aims at reconstructing the conductivity inside a physical body from boundary measurements of current and voltage at a finite number of contact electrodes. In many practical applications, the shape of the…

Numerical Analysis · Mathematics 2017-03-08 Nuutti Hyvönen , Helle Majander , Stratos Staboulis

The objective of electrical impedance tomography is to reconstruct the internal conductivity of a physical body based on measurements of current and potential at a finite number of electrodes attached to its boundary. Although the…

Numerical Analysis · Mathematics 2016-07-04 Nuutti Hyvönen , Vesa Kaarnioja , Lauri Mustonen , Stratos Staboulis

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

Magnetic Induction Tomography (MIT) is a promising modality for noninvasive imaging due to its contactless and nonionizing technology. In this imaging method, a primary magnetic field is applied by excitation coils to induce eddy currents…

Quantitative Methods · Quantitative Biology 2024-12-19 Mohammad Reza Yousefi , Amin Dehghani , Ali Asghar Amini , S. M. Mehdi Mirtalaei

Electrical Impedance Tomography (EIT) is a functional imaging method that is being developed for bedside use in critical care medicine. Aiming at improving the chest anatomical resolution of EIT images we developed a fuzzy model based on…

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

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

Electromagnetic (EM) imaging is an important tool for non-invasive sensing with low-cost and portable devices. One emerging application is EM stroke imaging, which enables early diagnosis and continuous monitoring of brain strokes.…

Signal Processing · Electrical Eng. & Systems 2025-09-08 Rui Guo , Yi Zhang , Yhonatan Kvich , Tianyao Huang , Maokun Li , Yonina C. Eldar

A novel and highly efficient computational framework for reconstructing binary-type images suitable for models of various complexity seen in diverse biomedical applications is developed and validated. Efficiency in computational speed and…

Optimization and Control · Mathematics 2024-02-09 Paul R. Arbic , Vladislav Bukshtynov

Electrical impedance tomography (EIT) is a non-invasive imaging method for recovering the internal conductivity of a physical body from electric boundary measurements. EIT combined with machine learning has shown promise for the…

We consider the problem of the detection of brain hemorrhages from three dimensional (3D) electrical impedance tomography (EIT) measurements. This is a condition requiring urgent treatment for which EIT might provide a portable and quick…

Numerical Analysis · Mathematics 2021-10-27 Valentina Candiani , Matteo Santacesaria
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