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In this paper we consider an inverse problem of determining a minimal surface embedded in a Riemannian manifold. We show under a topological condition that if $\Sigma$ is a $2$-dimensional embedded minimal surface, then the knowledge of the…

Analysis of PDEs · Mathematics 2023-10-24 Cătălin I. Cârstea , Matti Lassas , Tony Liimatainen , Leo Tzou

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

In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…

Analysis of PDEs · Mathematics 2020-05-20 Antonios Charalambopoulos , Vanessa Markaki , Drosos Kourounis

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…

Mathematical Physics · Physics 2009-12-03 Andrea A. Almasy

Electrical impedance tomography (EIT) is highly affected by modeling errors regarding electrode positions and the shape of the imaging domain. In this work, we propose a new inclusion detection technique that is completely independent of…

Analysis of PDEs · Mathematics 2018-10-11 Bastian Harrach , Eunjung Lee , Marcel Ullrich

This paper is concerned with an inverse obstacle problem for the Laplace's equation. The aim is to recover the constant conductivity coefficient in the equation and the boundary of a Dirichlet polygonal obstacle from a single pair of Cauchy…

Analysis of PDEs · Mathematics 2024-06-04 Xiaoxu Xu , Guanghui Hu

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

In electrical impedance tomography the electrical conductivity inside a physical body is computed from electro-static boundary measurements. The focus of this paper is to extend recent result for the 2D problem to 3D. Prior information…

Numerical Analysis · Mathematics 2016-01-20 Henrik Garde , Kim Knudsen

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…

Numerical Analysis · Mathematics 2016-10-06 Giovanni S. Alberti , Habib Ammari , Bangti Jin , Jin-Keun Seo , Wenlong Zhang

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

This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from…

Numerical Analysis · Mathematics 2020-01-13 Simon Hubmer , Kim Knudsen , Changyou Li , Ekaterina Sherina

In this paper, we address a classical case of the Calder\'on (or conductivity) inverse problem in dimension two. We aim to recover the location and the shape of a single cavity $\omega$ (with boundary $\gamma$) contained in a domain…

Analysis of PDEs · Mathematics 2015-09-10 Alexandre Munnier , Karim Ramdani

We study an inverse boundary value problem associated with $p$-Laplacian which is further perturbed by a linear second order term, defined on a bounded set $\Omega$ in $\R^n, n\geq 2$. We recover the coefficients at the boundary from the…

Analysis of PDEs · Mathematics 2024-01-12 Nitesh Kumar , Tanmay Sarkar , Manmohan Vashisth

We consider an inverse problem for a radiative transport equation (RTE) in which boundary sources and measurements are restricted to a single subset $E$ of the boundary of the domain $\Omega$. We show that this problem can be solved…

Analysis of PDEs · Mathematics 2020-01-31 Francis J. Chung

We study inverse conductivity problem for an anisotropic conductivity in $L^\infty$ in bounded and unbounded domains. Also, we give applications of the results in the case when Dirichlet-to-Neumann and Neumann-to-Dirichlet maps are given…

Analysis of PDEs · Mathematics 2007-05-23 Kari Astala , Matti Lassas , Lassi Paivarinta

We consider an inverse boundary value problem for the heat equation $\partial_t v = {\rm div}_x\,(\gamma\nabla_x v)$ in $(0,T)\times\Omega$, where $\Omega$ is a bounded domain of $R^3$, the heat conductivity $\gamma(t,x)$ admits a surface…

Analysis of PDEs · Mathematics 2015-06-15 Olivier Poisson

We consider the inverse obstacle scattering problem of determining both the shape and the "equivalent impedance" from far field measurements at a fixed frequency. In this work, the surface impedance is represented by a second order surface…

Numerical Analysis · Mathematics 2013-07-24 Laurent Bourgeois , Nicolas Chaulet , Houssem Haddar

We consider the inverse boundary value problem of recovering piecewise homogeneous elastic tensor and piecewise homogeneous mass density from a localized lateral Dirichlet-to-Neumann or Neumann-to-Dirichlet map for the elasticity equation…

Analysis of PDEs · Mathematics 2019-03-05 Cătălin I. Cârstea , Gen Nakamura , Lauri Oksanen

The electrical impedance tomography (EIT) problem of estimating the unknown conductivity distribution inside a domain from boundary current or voltage measurements requires the solution of a nonlinear inverse problem. Sparsity promoting…

Numerical Analysis · Mathematics 2024-05-27 Daniela Calvetti , Monica Pragliola , Erkki Somersalo

We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic…

Analysis of PDEs · Mathematics 2021-02-19 Zhengjian Bai , Huaian Diao , Hongyu Liu , Qingle Meng