Related papers: On second order shape optimization methods for ele…
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…
The Inverse Electrical Impedance Tomography (EIT) problem on recovering electrical conductivity tensor and potential in the body based on the measurement of the boundary voltages on the electrodes for a given electrode current is analyzed.…
Electrical impedance tomography (EIT) is an imaging modality in which the conductivity distribution inside a target is reconstructed based on voltage measurements from the surface of the target. Reconstructing the conductivity distribution…
Since shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations, we show how shape optimization techniques can also be applied to an interface identification problem…
In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a…
Using a rigorous method of matched asymptotic expansions, I derive the equation of motion of a small, compact body in an external vacuum spacetime through second order in the body's mass (neglecting effects of internal structure). The…
In this paper we analyze the relaxed form of a shape optimization problem with state equation $\{{array}{ll} -div \big(a(x)Du\big)=f\qquad\hbox{in}D \hbox{boundary conditions on}\partial D. {array}.$ The new fact is that the term $f$ is…
We introduce and study a new inverse problem for antiplane shear in elastic bodies with strain-gradient interfaces. The setting is a homogeneous isotropic elastic body containing an inclusion separated by a thin interface endowed with…
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…
In this paper, we study the affine phase retrieval problem, which aims to recover signals from the magnitudes of affine measurements. We develop second-order optimization methods based on Newton and Gauss-Newton iterations and establish…
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 derive a Sampling Method to solve the inverse shape problem of recovering an inclusion with a generalized impedance condition from electrostatic Cauchy data. The generalized impedance condition is a second-order…
This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…
Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman equations in the context of stochastic optimal control, or…
Let $(\Omega,g)$ be a smooth compact two-dimensional Riemannian manifold with boundary, $\Lambda_g: f\mapsto \partial_\nu u|_{\partial\Omega}$ its DN map, where $u$ obeys $\Delta_g u=0$ in $\Omega$ and $u|_{\partial \Omega}=f$. The Electric…
We propose an immersed boundary scheme for the numerical resolution of the Complete Electrode Model in Electrical Impedance Tomography, that we use as a main ingredient in the resolution of inverse problems in medical imaging. Such method…
In electrical impedance tomography, we aim to solve the conductivity within a target body through electrical measurements made on the surface of the target. This inverse conductivity problem is severely ill-posed, especially in real…
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…
The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…
We consider Inverse Electrical Impedance Tomography (EIT) problem on recovering electrical conductivity and potential in the body based on the measurement of the boundary voltages on the $m$ electrodes for a given electrode current. The…