Analysis of two linear sampling methods applied to electromagnetic imaging of buried objects

Abstract

We investigate two imaging methods to detect buried scatterers from electromagnetic measurements at a fixed frequency. The first one is the classical linear sampling method that requires the computation of Green's tensor for the background medium. This job can be numerically very costly for complex background geometries. The second one is an alternative approach based on the reciprocity gap functional that avoids the computation of Green's tensor but requires knowledge of both the electric and magnetic fields. Numerical examples are given showing the performance of both methods.

Target identification of buried coated objects

“…In general, this question is still open (However, see [1] for an answer to this question in the case of the scalar problem for a perfect conductor in homogeneous background using far field data). Numerical examples for similar reconstruction methods have shown in these cases that the computed regularized solution behaves in the way that the theory predicts [7], [9], [11], [15]. Note that the method determines D without any a priori knowledge of D , I or λ.…”

Target identification of buried coated objects

“…The use of electromagnetic fields to detect buried objects has a long history and continues to be an active area of research [3], [7], [8]. Of particular interest is the use of such methods to detect chemical waste deposits, examine urban infrastructure and locate landmines.…”

“…In order to overcome the problem of needing to compute the Green's function for the background media, a new version of the linear sampling method based on the reciprocity gap functional was introduced by Colton and Haddar [10] for the scalar case and by Cakoni, Fares and Haddar [7] for the vector case. However, in imagining nothing is free and the price paid for avoiding the need to compute the Green's function is that one now needs to measure both the electric and magnetic fields corresponding to time harmonic electric dipoles as incident fields.…”

“…However, in imagining nothing is free and the price paid for avoiding the need to compute the Green's function is that one now needs to measure both the electric and magnetic fields corresponding to time harmonic electric dipoles as incident fields. In the case when the buried object is a perfect conductor or a penetrable, anisotropic inhomogeneous medium, the efficaciousness of this approach to the imaging of buried objects was shown in [7]. The purpose of this paper is to consider the case FIORALBA CAKONI and DAVID COLTON 271 when the buried object is a perfect conductor that may be partially coated by a thin dielectric layer.…”

“…In particular, the inverse problem is now to not only determine the shape of the target but also whether or not the target is coated and if so the value of the surface impedance of the coating [13]. As in [7], we will consider the case when the electric and magnetic fields are both known on the entire boundary of an absorbing homogeneous region of the background media that is known a priori to contain the target. The case of an object buried in the earth is then handled by assuming that the part of the boundary below the surface of the earth is far away from the incident sources and hence we can assume that the total electric and magnetic fields are very small on this portion of the boundary.…”