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Electron tomography is a powerful tool for understanding the morphology of materials in three dimensions, but conventional reconstruction algorithms typically suffer from missing-wedge artifacts and data misalignment imposed by experimental…

Image and Video Processing · Electrical Eng. & Systems 2025-12-10 Cedric Lim , Corneel Casert , Arthur R. C. McCray , Serin Lee , Andrew Barnum , Jennifer Dionne , Colin Ophus

We study an elastic Calderon-type inverse problem: recover the mass density $\rho(x)$ in a bounded domain $\Omega\subset\mathbb{R}^3$ from the Neumann-to-Dirichlet map associated with the isotropic Lam\'e system…

Analysis of PDEs · Mathematics 2026-01-19 Huaian Diao , Mourad Sini , Ruixiang Tang

This paper proposes a nonlinear weighted anisotropic total variation (NWATV) regularization technique for electrical impedance tomography (EIT). The key idea is to incorporate the internal inhomogeneity information (e.g., edges of the…

Analysis of PDEs · Mathematics 2022-03-02 Yizhuang Song , Yanying Wang , Dong Liu

An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…

Numerical Analysis · Mathematics 2015-01-27 Sara Pollock

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…

Optimization and Control · Mathematics 2018-08-29 B. J. Adesokan , Kim Knudsen , Venkateswaran P. Krishnan , Souvik Roy

This paper is concerned with reconstruction issue of inverse obstacle problems governed by partial differential equations and consists of two parts. (i) The first part considers the foundation of the probe and enclosure methods for an…

Analysis of PDEs · Mathematics 2022-07-11 Masaru Ikehata

In this article, we consider the problem of finding the support of an inhomogenous possibly anisotropic inclusion in a background of constant electric conductivity from the electrical impedance tomography data at the boundary of a bounded…

Functional Analysis · Mathematics 2007-05-23 Erkki J. Somersalo

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

This paper aims to numerically solve the two-dimensional electrical impedance tomography (EIT) with Cauchy data. This inverse problem is highly challenging due to its severe ill-posed nature and strong nonlinearity, which necessitates…

Numerical Analysis · Mathematics 2025-07-22 Kai Li , Kwancheol Shin , Zhi Zhou

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

In this paper, we show that using measurements for different frequencies, and using ultrasound localized perturbations it is possible to extend the method of the imaging by elastic deformation developed by Ammari and al. [Electrical…

Analysis of PDEs · Mathematics 2010-04-21 Anna Rozanova-Pierrat

The multifrequency electrical impedance tomography consists in retrieving the conductivity distribution of a sample by injecting a finite number of currents with multiple frequencies. In this paper we consider the case where the…

Numerical Analysis · Mathematics 2017-04-18 Habib Ammari , Faouzi Triki , Chun-Hsiang Tsou

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

Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs conductivity distributions within a body from boundary measurements. However, EIT reconstruction is hindered by its ill-posed nonlinear inverse…

Image and Video Processing · Electrical Eng. & Systems 2024-09-11 Bowen Tong , Junwu Wang , Dong Liu

Electrical impedance tomography aims at reconstructing the interior electrical conductivity from surface measurements of currents and voltages. As the current-voltage pairs depend nonlinearly on the conductivity, impedance tomography leads…

Numerical Analysis · Mathematics 2017-05-31 Nuutti Hyvönen , Lauri Mustonen

Accurate determination of the complex effective permittivity is fundamental to optical material engineering, but it remains a critical metrology challenge for heterogeneous systems. In polymer blends and optical composites, scattering and…

Optics · Physics 2026-03-03 Proity Nayeeb Akbar

The multifrequency electrical impedance tomography is considered in order to image a conductivity inclusion inside a homogeneous background medium by injecting one current. An original spectral decomposition of the solution of the forward…

Analysis of PDEs · Mathematics 2016-09-23 Habib Ammari , Faouzi Triki

Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…

Optimization and Control · Mathematics 2025-08-08 Jie Gao , Cesare Molinari , Silvia Villa , Jingwei Liang

We derive exact reconstruction methods for cracks consisting of unions of Lipschitz hypersurfaces in the context of Calder\'on's inverse conductivity problem. Our first method obtains upper bounds for the unknown cracks, bounds that can be…

Analysis of PDEs · Mathematics 2024-05-24 Henrik Garde , Michael Vogelius

We study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution $\gamma$ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction…

Functional Analysis · Mathematics 2007-05-23 Kim Knudsen , Alexandru Tamasan