English
Related papers

Related papers: Electrical Impedance Tomography with Restricted Di…

200 papers

Modal expansions are useful to understand wave propagation in an infinite electromagnetic transmission line or waveguide. They can also be used to construct generalized Dirichlet-to-Neumann maps that can be used to provide artificial…

Analysis of PDEs · Mathematics 2023-02-24 Martin Halla , Peter Monk

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

Acousto-electric tomography (AET) is a hybrid imaging modality that combines electrical impedance tomography with focused ultrasound perturbations to obtain interior power density measurements, which provide additional information that can…

Analysis of PDEs · Mathematics 2026-03-31 Hjørdis Schlüter , Babak Maboudi Afkham

This paper presents a direct solution technique for the scattering of time-harmonic waves from a bounded region of the plane in which the wavenumber varies smoothly in space.The method constructs the interior Dirichlet-to-Neumann (DtN) map…

Numerical Analysis · Mathematics 2013-08-29 Adrianna Gillman , Alex Barnett , Per-Gunnar Martinsson

We consider the two-dimensional version of Calder\`on's problem. When the D-N map is assumed to be known up to an error level $\varepsilon_0$, we investigate how the resolution in the determination of the unknown conductivity deteriorates…

Analysis of PDEs · Mathematics 2018-01-16 Giovanni Alessandrini , Andrea Scapin

We study the numerical reconstruction problem in acousto-electric tomography of recovering the conductivity distribution in a bounded domain from interior power density data. We propose a numerical method for recovering discontinuous…

Optimization and Control · Mathematics 2019-02-20 Bolaji James Adesokan , Bjørn Jensen , Bangti Jin , Kim Knudsen

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 study of resonances of the Schr\"{o}dinger operator has a long-standing tradition in mathematical physics. Extensive theoretical investigations have explored the proximity of resonances to the real axis, their distribution, and bounds…

Numerical Analysis · Mathematics 2025-04-17 Bo Gong , Takumi Sato , Jiguang Sun , Xinming Wu

Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely…

Numerical Analysis · Mathematics 2016-05-25 Sarah Jane Hamilton , Jennifer L. Mueller , Melody Alsaker

In this paper we derive rigorously the derivative of the Dirichlet to Neumann map and of the Neumann to Dirichlet map of the conductivity equation with respect to movements of vertices of triangular conductivity inclusions. We apply this…

Analysis of PDEs · Mathematics 2020-12-29 E. Beretta , E. Francini , S. Vessella

The objective of electrical impedance tomography is to deduce information about the conductivity inside a physical body from electrode measurements of current and voltage at the object boundary. In this work, the unknown conductivity is…

Numerical Analysis · Mathematics 2015-04-28 Nuutti Hyvönen , Matti Leinonen

We study both the Riemannian and Lorentzian Calder\'on problem when a family of Dirichlet-to-Neumann maps are given for an open set of magnetic/electromagnetic potentials. For the Riemannian version, by allowing small perturbations of the…

Analysis of PDEs · Mathematics 2025-12-19 Yuchao Yi

The original Calder\'on problem consists in recovering the potential (or the conductivity) from the knowledge of the related Neumann to Dirichlet map (or Dirichlet to Neumann map). Here, we first perturb the medium by injecting small-scaled…

Analysis of PDEs · Mathematics 2025-07-11 Ahcene Ghandriche , Mourad Sini

We establish two commutator estimates for the Dirichlet-to-Neumann map associated with a second-order elliptic system in divergence form in Lipschitz domains. Our approach is based on Dahlberg's bilinear estimates.

Analysis of PDEs · Mathematics 2013-08-29 Zhongwei Shen

Electrical impedance tomography (EIT) uses current-voltage measurements on the surface of an imaging subject to detect conductivity changes or anomalies. EIT is a promising new technique with great potential in medical imaging and…

Numerical Analysis · Mathematics 2018-11-19 Bastian Harrach , Marcel Ullrich

It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the…

Numerical Analysis · Mathematics 2022-03-23 Thuy T. Le , Michael V. Klibanov , Loc H. Nguyen , Anders Sullivan , Lam Nguyen

We consider an inverse shape problem arising in electrical impedance tomography (EIT) for nondestructive testing, in which interior defects are modeled through Robin transmission conditions. Unlike classical formulations, we impose Robin…

Numerical Analysis · Mathematics 2026-01-19 Rafael Ceja Ayala , Malena I. Español , Govanni Granados

A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured…

Numerical Analysis · Mathematics 2008-09-24 Hua Shan , M. V. Klibanov , Jianzhong Su , Natee Pantong , Hanli Liu

This article shows that knowledge of the Dirichlet-Neumann map on certain subsets of the boundary for input functions supported roughly on the rest of the boundary can be used to determine a magnetic Schr\"{o}dinger operator. With some…

Analysis of PDEs · Mathematics 2011-11-30 Francis J. Chung

Electrical Impedance Tomography (EIT) is a non-invasive medical imaging method that reconstructs electrical conductivity mediums from boundary voltage-current measurements, but its severe ill-posedness renders direct operator learning with…

Numerical Analysis · Mathematics 2026-01-14 Amit Bhat , Ke Chen , Chunmei Wang