Related papers: Determining conductivity and embedded obstacles fr…
We prove \emph{global} uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be isotropic and nontrivial in the exterior of the domain,…
We consider an inverse boundary value problem for the equation $\nabla\cdot(\sigma-i\omega\epsilon)\nabla u=0$ in a given bounded domain $\Omega$ at a fixed $\omega>0$. $\sigma$ and $\epsilon$ denote the conductivity and permittivity of the…
We discuss the inverse problem of determining the possible presence of an (n-1)-dimensional crack \Sigma in an n-dimensional body \Omega with n > 2 when the so-called Dirichlet-to-Neumann map is given on the boundary of \Omega. In…
Imposing either Dirichlet or Neumann boundary conditions on the boundary of a smooth bounded domain $\Omega$, we study the perturbation incurred by the voltage potential when the conductivity is modified in a set of small measure. We…
We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of some general class of magnetic field and…
Magneto-acousto-electric tomography (MAET) combines ultrasound with a static magnetic field to infer the electrical conductivity of an object. In this paper, we present a rigorous quasi-static mathematical model for MAET with magnetic field…
An inverse problem of identifying locations and certain properties of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on a part of the boundary is studied. Using as weights particular…
We consider the inverse shape and parameter problem for detecting corrosion from partial boundary measurements. This problem models the non-destructive testing for a partially buried object from electrostatic measurements on the accessible…
The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…
We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic…
Electrical impedance tomography (EIT) is a noninvasive medical imaging modality utilizing the current-density/voltage data measured on the surface of the subject. Calder\'on's method is a relatively recent EIT imaging algorithm that is…
We construct counterexamples for the partial data inverse problem for the fractional conductivity equation in all dimensions on general bounded open sets. In particular, we show that for any bounded domain $\Omega \subset \mathbb{R}^n$ and…
A novel computational, non-iterative and noise-robust reconstruction method is introduced for the planar anisotropic inverse conductivity problem. The method is based on bypassing the unstable step of the reconstruction of the values of the…
The Electrical Resistance Tomography (ERT) technique is applied to the measurement of sheet conductance maps of both uniform and patterned conductive thin films. Images of the sheet conductance spatial distribution, and local conductivity…
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…
In this paper, we will discuss the use of a Sampling Method to reconstruct impenetrable inclusions from Electrostatic Cauchy data. We consider the case of a perfectly conducting and impedance inclusion. In either case, we show that the…
The inverse problem in Acousto-Electric tomography concerns the reconstruction of the electric conductivity in a domain from knowledge of the power density function in the interior of the body. This interior power density results from…
This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint…
We establish stability inequalities of an inverse obstacle problem for the magnetic Schr\"odinger equation. We mainly study the problem of reconstructing an unknown function defined on the obstacle boundary from two measurements performed…
In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the…