Related papers: Reconstruction of shapes and refractive indices fr…
The problem to be studied in this work is within the context of coefficient identification problems for the wave equation. More precisely, we consider the problem of reconstruction of the refractive index (or equivalently, the dielectric…
We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary…
We consider a coefficient inverse problem for the dielectric permittivity in Maxwell's equations, with data consisting of boundary measurements of one or two backscattered or transmitted waves. The problem is treated using a Lagrangian…
We consider a two-stage numerical procedure for imaging of objects buried in dry sand using time-dependent backscattering experimental radar measurements. These measurements are generated by a single point source of electric pulses and are…
This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielectric constants, electric conductivities and shapes of front…
We present a posteriori error estimates for finite element approximations in a minimization approach to a coefficient inverse problem. The problem is that of reconstructing the dielectric permittivity $\varepsilon =…
This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…
We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known…
We consider the problem of reconstruction of dielectrics from blind backscattered experimental data. Experimental data were collected by a device, which was built at University of North Carolina at Charlotte. This device sends electrical…
We perform extended studies of an adaptive finite element method applied to the reconstruction of shapes of buried objects from experimental backscattering data. We use experimental data which are collected by a microwave scattering…
We propose in this paper a globally numerical method to solve a phaseless coefficient inverse problem: how to reconstruct the spatially distributed refractive index of scatterers from the intensity (modulus square) of the full complex…
The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…
This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…
We consider the numerical reconstruction of the spatially dependent conductivity coefficient and the source term in elliptic partial differential equations in a two-dimensional convex polygonal domain, with the homogeneous Dirichlet…
This paper concerns the quantitative step of the medical imaging modality Thermo-acoustic Tomography (TAT). We model the radiation propagation by a system of Maxwell's equations. We show that the index of refraction of light and the…
We present new method for the numerical reconstruction of the variable refractive index of multi-layered circular weakly guiding dielectric waveguides using the measurements of the propagation constants of their eigenwaves. Our numerical…
We consider the inverse problem of the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions of the Maxwell's system in 3D with limited boundary observations of the electric field. The theoretical…
We present a variational optimization approach for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and conductivity functions in time-dependent Maxwell's system using limited…
For the first time, we develop in this paper the globally convergent convexification numerical method for a Coefficient Inverse Problem for the 3D Helmholtz equation for the case when the backscattering data are generated by a point source…
We examine the refractive index from the viewpoint of modern first-principles materials physics. We first argue that the standard formula, $n^2 = \varepsilon_{\mathrm r} \mu_{\mathrm r}$, is generally in conflict with fundamental principles…