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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

This article proposes a process to reconstruct a Riemann surface with boundary equipped with a conductivity tensor from its boundary and its Dirichlet-Neumann operator. When initial data comes from a two dimensional real Riemannian oriented…

Complex Variables · Mathematics 2017-05-09 Vincent Michel

In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to…

Analysis of PDEs · Mathematics 2018-03-20 Elena Beretta , Stefano Micheletti , Simona Perotto , Matteo Santacesaria

The aim of Electrical Impedance Tomography (EIT) is to determine the electrical conductivity distribution inside a domain by applying currents and measuring voltages on its boundary. Mathematically, the EIT reconstruction task can be…

Numerical Analysis · Mathematics 2024-05-07 Monica Pragliola , Daniela Calvetti , Erkki Somersalo

In this paper we consider the inverse problem of determining on a compact Riemannian manifold the metric tensor in the wave equation with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the…

Analysis of PDEs · Mathematics 2021-02-11 Mourad Bellassoued

An efficient numerical method is proposed for computing the Dirichlet-to-Neumann (DtN) map associated with the exterior Dirichlet problem for the two-dimensional Helmholtz equation with an inhomogeneous term. The exterior solution is…

Numerical Analysis · Mathematics 2026-03-17 Takemi Shigeta

We consider an inverse problem of location identification of small conductivity inhomogeneity inside a conductor via boundary measurements which occurs in the EIT (Electrical Impedance Tomography). For this purpose, we derive topological…

Classical Physics · Physics 2013-08-20 Won-Kwang Park

This work establishes a framework for solving inverse boundary problems with the geodesic based quadratic Wasserstein distance ($W_{2}$). A general form of the Fr\'echet gradient is systematically derived by optimal transportation (OT)…

Numerical Analysis · Mathematics 2022-10-31 Gang Bao , Yixuan Zhang

A new version of the convexification method is developed analytically and tested numerically for a 1-D coefficient inverse problem in the frequency domain. Unlike the previous version, this one does not use the so-called "tail function",…

Numerical Analysis · Mathematics 2018-10-17 Michael V. Klibanov , Aleksandr E. Kolesov , Anders Sullivan , Lam Nguyen

We show that an electric potential and magnetic field can be uniquely determined by partial boundary measurements of the Neumann-to-Dirichlet map of the associated magnetic Schr\"{o}dinger operator. This improves upon previous results of…

Analysis of PDEs · Mathematics 2014-02-19 Francis J. Chung

The Dirichlet-to-Neumann map for differential forms on a Riemannian manifold with boundary is a generalization of the classical Dirichlet-to-Neumann map which arises in the problem of Electrical Impedance Tomography. We synthesize the two…

Differential Geometry · Mathematics 2019-10-23 Vladimir Sharafutdinov , Clayton Shonkwiler

In this paper, we present a discussion on the algorithms design of Electrical Impedance Tomography (EIT) for biomedical applications. Based on the Maxwell differential equations and the derived the finite element(FE) linear equations, we…

Signal Processing · Electrical Eng. & Systems 2019-01-23 Mingyong Zhou , Hongyu Zhu

This document reports an Open 2D Electrical Impedance Tomography (EIT) data set. The EIT measurements were collected from a circular body (a flat tank filled with saline) with various choices of conductive and resistive inclusions. Data are…

We consider the Klein-Gordon equation on asymptotically anti-de Sitter spacetimes, and show that the forward Dirichlet-to-Neumann map (or scattering matrix) is a fractional power of the boundary wave operator modulo lower order terms in the…

Analysis of PDEs · Mathematics 2026-03-17 Alberto Enciso , Gunther Uhlmann , Michał Wrochna

For a compact connected Riemannian manifold with smooth boundary, by computing the full symbol of the elastic Dirichlet-to-Neumann map, we prove that the elastic Dirichlet-to-Neumann map can uniquely determine the partial derivatives of all…

Differential Geometry · Mathematics 2024-07-09 Xiaoming Tan

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

We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in $\mathbb{R}^3$ via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann…

Analysis of PDEs · Mathematics 2017-02-10 Maarten V. de Hoop , Gen Nakamura , Jian Zhai

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

We study the linearization of the Dirichlet-to-Neumann map for Poincar\'e-Einstein metrics in even dimensions on an arbitrary compact manifold with boundary. By fixing a suitable gauge, we make the linearized Einstein equation elliptic. In…

Differential Geometry · Mathematics 2009-05-18 Fang Wang

We consider a linearized inverse boundary value problem for the elasticity system. From the linearized Dirichlet-to-Neumann map at zero frequency, we show that a transversely isotropic perturbation of a homogeneous isotropic elastic tensor…

Analysis of PDEs · Mathematics 2019-01-08 Yang Yang , Jian Zhai