Reconstruction of the Refractive Index from Experimental Backscattering Data Using a Globally Convergent Inverse Method

Abstract

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 constant) of an inhomogeneous medium using one backscattering boundary measurement. The goal of this paper is to analyze the performance of a globally convergent algorithm of Beilina and Klibanov on experimental data acquired in the Microwave Laboratory at University of North Carolina at Charlotte. The main challenge working with experimental data is the the huge misfit between these data and computationally simulated data. We present data pre-processing steps to make the former somehow look similar to the latter. Results of both non-blind and blind targets are shown indicating good reconstructions even for high contrasts between the targets and the background medium.

An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

“…We only remark that unlike certain applications, e.g. some significant mismatch has been reported in [1,23,27] between experimental data of electromagnetic waves propagating in a non-attenuating medium and data produced by idealized computational simulations, in inverse heat conduction the mathematical models have been shown to perform much better in industrial applications with actual real measured data, [9]. 30, 025002 (24 pages).…”

A globally convergent numerical method for a coefficient inverse problem for a parabolic equation

“…However, it might be possible to invent such a method which would satisfy the requirement (a) for at least one MCIP. The latter was done in works of Klibanov in 2008-2014 [1][2][3][4][5][6][7][8]. Furthermore, their method was completely verified on experimental data [3][4][5][6][7][8].…”

“…Thus, we can assume that the function g(x, t) is known at the entire surface, see, e.g. a similar situation for the case of real measurements in [3][4][5][6][7][8]. We do not discuss here a specific way of that interpolation.…”

“…The latter was done in works of Klibanov in 2008-2014 [1][2][3][4][5][6][7][8]. Furthermore, their method was completely verified on experimental data [3][4][5][6][7][8]. Recently Chow and Zou [9] have studied the Beilina-Klibanov method numerically for a MCIP for a hyperbolic equation, which is different from the one studied in [1][2][3][4][5][6][7][8].…”

Adaptive finite element method in nanophotonic simulations

“…Thus, similarly to [4,9], we consider the propagation of electromagnetic waves with a field polarization and model the wave propagation by the following scalar wave equation:…”