相关论文: The inverse conductivity problem with an imperfect…
We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so--called Dirichlet-to-Neumann map is locally given on a non empty portion $\Gamma$ of the boundary…
We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work \cite{DKSaU}, it was shown that a metric in a…
A positive function (conductivity) on the edges of a graph induces the Dirichlet-to- Neumann map between boundary values of harmonic functions. The inverse conductivity problem is to find the conductivity from the Dirichlet-to-Neumann map.…
In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…
This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…
We prove a global uniqueness result for the Calder\'{o}n inverse problem for a general quasilinear isotropic conductivity equation on a bounded open set with smooth boundary in dimension $n\ge 3$. Performing higher order linearizations of…
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…
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…
We study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution $\gamma$ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction…
In this paper we consider inverse problems for resistor networks and for models obtained via the Finite Element Method (FEM) for the conductivity equation. These correspond to discrete versions of the inverse conductivity problem of…
This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…
We consider the imaging of anisotropic conductivity tensors $\gamma=(\gamma_{ij})_{1\leq i,j\leq 2}$ from knowledge of several internal current densities $\mathcal{J}=\gamma\nabla u$ where $u$ satisfies a second order elliptic equation…
In this paper, we consider the inverse scattering problem associated with an anisotropic medium with a conductive boundary. We will assume that the corresponding far-field pattern is known/measured and we consider two inverse problems.…
We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so-called Neumann-to-Dirichlet map is locally given on a non empty curved portion $\Sigma$ of the…
We consider the inverse problem of recovering an isotropic electrical conductivity from interior knowledge of the magnitude of one current density field generated by applying current on a set of electrodes. The required interior data can be…
In this paper we study an inverse problem for fractional anisotropic conductivity. Our nonlocal operator is based on the well-developed theory of nonlocal vector calculus, and differs substantially from other generalizations of the…
An inverse boundary value problem for the Helmholtz equation in a bounded domain is considered. The problem is to extract information about an unknown obstacle embedded in the domain with unknown impedance boundary condition (the Robin…
We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate…
We study an inverse problem for nonlinear elliptic equations modelled after the p-Laplacian. It is proved that the boundary values of a conductivity coefficient are uniquely determined from boundary measurements given by a nonlinear…
This paper is concerned with reconstruction issue of some typical inverse problems and consists of three parts. First a framework of the enclosure method for an inverse source problem governed by the Helmholtz equation at a fixed wave…