English
Related papers

Related papers: An inverse conductivity problem in multifrequency …

200 papers

The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it…

Analysis of PDEs · Mathematics 2018-09-20 Henrik Garde , Stratos Staboulis

In this article we study the inverse problem of recovering a space-dependent coefficient of the Moore-Gibson-Thompson (MGT) equation, from knowledge of the trace of the solution on some open subset of the boundary. We obtain the Lipschitz…

Analysis of PDEs · Mathematics 2021-11-08 Rogelio Arancibia , Rodrigo Lecaros , Alberto Mercado , Sebastián Zamorano

In Gel'fand's inverse problem, one aims to determine the topology, differential structure and Riemannian metric of a compact manifold $M$ with boundary from the knowledge of the boundary $\partial M,$ the Neumann eigenvalues $\lambda_j$ and…

Analysis of PDEs · Mathematics 2025-04-02 Dmitri Burago , Sergei Ivanov , Matti Lassas , Jinpeng Lu

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

The use of the Factorization method for Electrical Impedance Tomography has been proved to be very promising for applications in the case where one wants to find inhomogeneous inclusions in a known background. In many situations, the…

Analysis of PDEs · Mathematics 2015-06-18 Nicolas Chaulet , Simon Arridge , Timo Betcke , David Holder

The size estimation problem in electrical impedance tomography is considered when the conductivity is a complex number and the body is two-dimensional. Upper and lower bounds on the volume fraction of the unknown inclusion embedded in the…

Analysis of PDEs · Mathematics 2013-10-10 Hyeonbae Kang , Kyoungsun Kim , Hyundae Lee , Xiaofei Li , Graeme W. Milton

We provide a mathematical analysis and a numerical framework for Lorentz force electrical conductivity imaging. Ultrasonic vibration of a tissue in the presence of a static magnetic field induces an electrical current by the Lorentz force.…

Analysis of PDEs · Mathematics 2014-01-13 Habib Ammari , Pol Grasland-Mongrain , Pierre Millien , Laurent Seppecher , Jin-Keun Seo

A path integral Monte Carlo method (PIMC) based on Feynman-Kac formula for mixed boundary conditions of elliptic equations is proposed to solve the forward problem of electrical impedance tomography (EIT) on the boundary to obtain…

Numerical Analysis · Mathematics 2019-08-01 Yijing Zhou , Wei Cai

We consider the inverse problem of identifying an unknown inclusion contained in an elastic body by the Dirichlet-to-Neumann map. The body is made by linearly elastic, homogeneous and isotropic material. The Lam\'e moduli of the inclusion…

Analysis of PDEs · Mathematics 2016-05-31 Giovanni Alessandrini , Michele Di Cristo , Antonino Morassi , Edi Rosset

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

This paper proposes a novel approach to reconstruct changes in a target conductivity from electrical impedance tomography measurements. As in the conventional difference imaging, the reconstruction of the conductivity change is based on…

Computational Physics · Physics 2014-03-27 Dong Liu , Ville Kolehmainen , Samuli Siltanen , Anne maria Laukkanen , Aku Seppanen

We are concerned with the Calder\'on inverse inclusion problem, where one intends to recover the shape of an inhomogeneous conductive inclusion embedded in a homogeneous conductivity by the associated boundary measurements. We consider the…

Analysis of PDEs · Mathematics 2021-05-26 Hongyu Liu , Chun-Hsiang Tsou , Wei Yang

This paper is devoted to the analysis of a second order method for recovering the \emph{a priori} unknown shape of an inclusion $\omega$ inside a body $\Omega$ from boundary measurement. This inverse problem - known as electrical impedance…

Optimization and Control · Mathematics 2007-05-23 Lekbir Afraites , Marc Dambrine , Djalil Kateb

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…

Geophysics · Physics 2012-05-29 Nick Polydorides , Alireza Aghasi , Eric L. Miller

The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme…

Analysis of PDEs · Mathematics 2021-02-05 Valentina Candiani , Jérémi Dardé , Henrik Garde , Nuutti Hyvönen

In this paper we provide a representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction in a simplified {\em monodomain model} describing the electric activity of the…

Analysis of PDEs · Mathematics 2014-12-24 Elena Beretta , M. Cristina Cerutti , Andrea Manzoni , Dario Pierotti

This paper develops 'covariant tomography', a local framework for solving Inverse Boundary Value Problems (IBVP) for parallel transport equation on star-shaped domains. By integrating geometric decomposition with specific interior…

Mathematical Physics · Physics 2026-03-03 Radosław Antoni Kycia

This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…

Analysis of PDEs · Mathematics 2018-08-17 Gang Bao , Peijun Li , Yue Zhao

Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity…

Machine Learning · Computer Science 2023-10-31 Derick Nganyu Tanyu , Jianfeng Ning , Andreas Hauptmann , Bangti Jin , Peter Maass

Several newly developing hybrid imaging methods (e.g., those combining electrical impedance or optical imaging with acoustics) enable one to obtain some auxiliary interior information (usually some combination of the electrical conductivity…

Analysis of PDEs · Mathematics 2013-02-25 Peter Kuchment , Dustin Steinhauer