On the imaging of thin dielectric inclusions buried within a half-space

Abstract

Motivated from the application area of imaging of anti-personnel mines completely embedded in the homogeneous medium, the problem of noniterative imaging of thin dielectric inclusions buried within a dielectric halfspace is considered. For that purpose, an imaging algorithm operated at several frequencies is proposed. It is based on the asymptotic expansion formula of the scattering amplitude in the presence of the inclusions. Various numerical examples illustrate how the method behaves.

Non-Iterative Imaging of Thin Electromagnetic Inclusions From Multi-Frequency Response Matrix

“…, M , and of small magnitude at x ∈ R 2 \Γ. Unfortunately, image function (8) at single frequency offers an image with poor resolution [3,23] (also see Figure 4). In order to improve the imaging performance, we suggest a normalized image function at several frequencies {ω f : f = 1, 2, .…”

“…Now, we end this section with the following example. Throughout some results in [4,23], it has been observed that MUSIC-type algorithm yields poorer results under the limited range of incident and observation directions. However, the proposed imaging algorithm is available for only a limited range of incident and observation directions.…”

“…However, in the imaging of thin inclusion of both dielectric and magnetic contrast with respect to the embedding homogeneous space R 2 case, one obtains a poor result so that an improvement is required. Recently, an effective and robust multifrequency algorithm has been proposed so as to find the location of small perfectly conducting cracks [3] and dielectric thin inclusions within a homogeneous half-space [23], but a suitable algorithm for extended inclusions of both dielectric and magnetic contrast is still expected.…”

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

“…To find a good initial guess, alternative non-iterative reconstruction algorithms have been developed, such as the MUltiple SIgnal Classification (MUSIC)-type algorithm [5,23,25], linear sampling method [8,12], topological derivative strategy [3,6,18,21,22], linear-δ, vector and multipolarized approaches [29,30], and the multifrequency based algorithm such as Kirchhoff and subspace migrations [2,4,15,19,20,24]. Among them, although the multi-frequency based subspace migration has exhibited potential as a non-iterative imaging technique, a mathematical identification of its structure needs to be performed for its heuristical applications, which is the motivation behind.…”

“…, M . Therefore, W(r; ω) will plots peaks of magnitude of 1 at r = r m ∈ Σ m , and of small magnitude at r / ∈ Σ m (see [4,19,20,24]). Complete algorithm is summarized in Algorithm 1.…”