Fast Imaging of Thin, Curve-Like Electromagnetic Inhomogeneities without a Priori Information

Won-Kwang Park

doi:10.3390/math8050799

Abstract

It is well-known that subspace migration is a stable and effective non-iterative imaging technique in inverse scattering problem. However, for a proper application, a priori information of the shape of target must be estimated. Without this consideration, one cannot retrieve good results via subspace migration. In this paper, we identify the mathematical structure of single- and multi-frequency subspace migration without any a priori of unknown targets and explore its certain properties. This is based on the fact that elements of so-called multi-static response (MSR) matrix can be represented as an asymptotic expansion formula. Furthermore, based on the examined structure, we improve subspace migration and consider the multi-frequency subspace migration. Various results of numerical simulation with noisy data support our investigation.

Highlights

There exists a considerable amount of interesting inverse scattering problems concerned with the retrieval of crack-like defects completely embedded in a medium from measurement data
The purpose of this paper is to apply subspace migration for imaging of a thin crack-like electromagnetic inhomogeneity located in the two-dimensional homogeneous space without any a priori information of inhomogeneity
The thickness h of thin inclusions Γ j is set to 0.015 and the imaging domain Ω is selected as Ω = [−1, 1] × [−1, 1]

Summary

Introduction

There exists a considerable amount of interesting inverse scattering problems concerned with the retrieval of crack-like defects completely embedded in a medium from measurement data (for related works, see [1,2,3,4,5,6] and references therein) This problem is considered an interesting and important issue because it is closely related to human life. One will need large computational costs, encounter non-convergence issue, or obtain a local minimizer instead of true solution For this reason, generation of a good initial guess without any a priori information of target must to be considered.

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Results

Conclusion