Inverse electromagnetic scattering in a two-layered medium with an application to mine detection

Abstract

The detection of metallic objects is an important application in state-of-the-art security technology. In particular, for humanitarian mine detection the task is to detect objects that are buried in soil. Usually hand-held mine detectors create an electromagnetic pulse via a current in some wire loop and evaluate the scattered electromagnetic field via induction in a receiver loop that is moved together with the sender loop. This receiver signal can then be employed in identifying the location and the shape of metallic objects. Here, we model the full electromagnetic scattering problem in a two-layered medium from a perfectly conducting obstacle using boundary integral equations. The scattered field is modeled via a boundary layer approach and for its kernel the Green's matrix for the two-layered medium is constructed. We establish uniqueness and existence for the solution of the corresponding boundary integral equation.In the second part of the paper, we employ a direct search method for parameter estimation to find the location and size of some simple metallic objects from measurements of the induced voltage for a number of sender-receiver-loop positions.

Structure Analysis of Single- And 2 Multi-Frequency Subspace Migrations in 3 Inverse Scattering Problems

“…We now determine the structure of imaging function (9). Before proceeding, we assume that scatterers are well resolved by the measurement array and based on the Rayleigh resolution limit from far-field data, any detail less than one-half of the wavelength cannot be seen so that scatterers are well-separated to each other, refer to [2].…”

“…If the total number of incident and observation directions N is sufficiently large and satisfies N > M , then the imaging function (9) can be represented as follows:…”

“…In research fields such as physics, medical science, and materials engineering, this is an interesting and important problem. Related works can be found in [2,7,[9][10][11]32] and references therein. In order to solve this problem, various algorithms for finding the locations and/or shapes of targets have been accordingly developed.…”

“…In many research studies [1,7,9,13,17,26], the shape reconstruction method is based on Newton-type iterative algorithms. However, for a successful shape reconstruction using these algorithms, the iterative procedure must begin with a good initial guess that is close to the unknown target because it highly depends on the initial guess; for more details, refer to [16,26].…”

An inverse scattering problem for the time‐dependent Maxwell equations: nonlinear optimization and model‐order reduction

“…Let us have a closer look to system (6). The Lagrange multipliers satisfy Maxwell-like equations, in which the signs of the time derivatives are opposite with respect to the standard curl equations.…”