Related papers: Determining conductivity and embedded obstacles fr…
Working within the class of piecewise constant conductivities, the inverse problem of electrical impedance tomography can be recast as a shape optimization problem where the discontinuity interface is the unknown. Using Gr\"oger's…
An inverse obstacle problem for the wave equation in a two layered medium is considered. It is assumed that the unknown obstacle is penetrable and embedded in the lower half-space. The wave as a solution of the wave equation is generated by…
This paper is concerned with a new type of inverse obstacle problem governed by a variable-order time-fraction diffusion equation in a bounded domain. The unknown obstacle is a region where the space dependent variable-order of fractional…
In this paper, we use the theory of symmetric Dirichlet forms to derive Feynman-Kac formulae for the forward problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities corresponding to different…
We establish H\"older stability of an inverse hyperbolic obstacle problem. Mainly, we study the problem of reconstructing an unknown function defined on the boundary of the obstacle from two measurements taken on the boundary of a domain…
This short note considerably simplifies a reconstruction method by the author (Comm. PDE, 45(9):1118--1133, 2020), for reconstructing piecewise constant layered conductivities (PCLC) from partial boundary measurements in electrical…
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 consider the inverse problem for the wave equation on a compact Riemannian manifold or on a bounded domain of $\R^n$, and generalize the concept of {\em domain of influence}. We present an efficient minimization algorithm to compute the…
Consider the scattering of time-harmonic point sources by an infinite locally rough interface with bounded obstacles embedded in the lower half-space. The model problem is first reduced to an equivalent integral equation formulation defined…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…
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…
In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology. The goal is the detection…
In this paper we estimate the size of a measurable inclusion in terms of power measurements for a single applied boundary current. This problem arises in medical imaging for the screening of organs. For this kind of problem one has to deal…
In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…
We consider the problem of the recovery of a Robin coefficient on a part $\gamma \subset \partial \Omega$ of the boundary of a bounded domain $\Omega$ from the principal eigenvalue and the boundary values of the normal derivative of the…
We present a procedure for recovering the conformal factor of an anisotropic conductivity matrix in a known conformal class in a domain in Euclidean space of dimension greater than or equal to 2. The method requires one internal…
We present a reconstruction algorithm for recovering both "magnetic-hard" and "magnetic-soft" obstacles in a background domain with known isotropic medium from the boundary impedance map. We use in our algorithm complex geometric optics…
Electrical impedance tomography (EIT) enables non-invasive, spatially continuous reconstruction of internal conductivity distributions, providing full field sensing beyond conventional point measurements. Here, we report the first in situ…
We present a comprehensive mathematical study of the Magneto-Telluric (MT) method, on bounded domain in $\mathbb{R}^3$. We show that electrical conductivity and magnetic permeability, assumed to be $C^2$, can be uniquely recovered from MT…
We consider an inverse boundary value problem for Maxwell's equations, which aims to recover the electromagnetic material properties of a body from measurements on the boundary. We show that a Lipschitz continuous conductivity, electric…