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

Abstract

Abstract-Although MUSIC (MUltiple SIgnal Classification)-type algorithm has shown feasibilities as a non-iterative imaging technique of thin penetrable electromagnetic inclusion from its far-field multistatic response (MSR) matrix, it induces a poor result whenever one tries to obtain such inclusion of both dielectric and magnetic contrast with respect to the embedding homogeneous space R 2 case. In this paper, we develop an improved non-iterative imaging algorithm based on the modeling of multi-frequency MSR matrix according to a rigorous asymptotic expansion of the scattering amplitude. Numerical examples exhibit that presented algorithm performs satisfactorily for single and multiple thin inclusions, even with a fair amount of random noise.

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

“…Several researches in [2,4,19,20] have confirmed on the basis of Statistical Hypothesis Testing and numerical experiments that the multi-frequency imaging function (11) is an improved version of the single-frequency version (10). The reason for this is discussed as follows.…”

“…In Section 2, we briefly review the two-dimensional direct scattering problem, and an asymptotic expansion formula for far-field patterns, and introduce the imaging function introduced in [19]. In Section 3, we analyze the single-and multi-frequency based imaging functions and discuss their properties.…”

“…, 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.…”

“…The imaging algorithm introduced in [19] used the structure of a singular vector of the Multi-Static (3) with observation number p and incident number q.…”

“…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.…”