Topological derivative strategy for one-step iteration imaging of arbitrary shaped thin, curve-like electromagnetic inclusions

Park, Won-Kwang

doi:10.1016/j.jcp.2011.10.014

Cited by 49 publications

(63 citation statements)

References 23 publications

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“…Note that topological derivative based non-iterative imaging algorithm has been developed but considered only in full-aperture inverse scattering problems, refer to [2,12,13,15,17,18]. Motivated from this fact, an analysis of topological derivative imaging function in the limited-aperture problem should be an interesting work.…”

Section: Resultsmentioning

confidence: 99%

Properties of Music-Type Algorithm for Imaging of Thin Dielectric Inhomogeneity in Limited-View Inverse Scattering Problem

Park

2014

PIER M

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Abstract-It is well known that a Multiple Signal Classification (MUSIC)-type algorithm yields good results in the imaging of thin dielectric inhomogeneity for full-view inverse scattering problems. In contrast, it yields a poor result in limited-view inverse scattering problems. In this paper, we verify the reason for the above by establishing a relationship between a MUSIC-type imaging function and the Bessel functions of the integer order of the first kind. This verification is based on the asymptotic expansion formula for thin dielectric inhomogeneity. Various numerical examples are discussed for confirming our verification.

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Section: Resultsmentioning

confidence: 99%

Properties of Music-Type Algorithm for Imaging of Thin Dielectric Inhomogeneity in Limited-View Inverse Scattering Problem

Park

2014

PIER M

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“…This concept was originally developed for the shape optimization problem, but its application to rapid shape reconstruction has only recently been proven. Related works can be found in [5,10,12,13,14,24,25,27,30,31,38] and references therein. One of the advantages of topological derivative concept is that it does not require a large amount of many incident field data; however, a reduction in the amount of this data has been reported to result in poor resolution of the reconstructed shape.…”

Section: Introductionmentioning

confidence: 99%

“…Based on recent research [5,10,30,31], a sufficiently large number of incident directions are required to obtain a good result. This means that if M is small, an image with poor resolution will be reconstructed.…”

Section: Multi-frequency Topological Derivative: Introduction and Anamentioning

confidence: 99%

Performance analysis of multi-frequency topological derivative for reconstructing perfectly conducting cracks

Park

2017

Journal of Computational Physics

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This paper concerns a fast, one-step iterative technique of imaging extended perfectly conducting cracks with Dirichlet boundary condition. In order to reconstruct the shape of cracks from scattered field data measured at the boundary, we introduce a topological derivativebased electromagnetic imaging function operated at several nonzero frequencies. The properties of the imaging function are carefully analyzed for the configurations of both symmetric and non-symmetric incident field directions. This analysis explains why the application of incident fields with symmetric direction operated at multiple frequencies guarantees a successful reconstruction. Various numerical simulations with noise-corrupted data are conducted to assess the performance, effectiveness, robustness, and limitations of the proposed technique.

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“…It is worthwhile precising that the problem of detecting small electromagnetic inclusions has been previously studied by using MUSIC-type algorithms [6], time reversal and phase conjugation techniques [36][37][38], reverse time migration [19], topological derivative based imaging [30], and asymptotic expansion techniques [8,9]. For the imaging of thin electromagnetic inclusions and cracks in a two dimensional setting, we refer the reader to [33,34] for instance. We will restrict ourselves only to the detection of the inclusion and will not discuss its morphology (shape, size and material properties) in this paper.…”

Section: Introductionmentioning

confidence: 99%

Stability and Resolution Analysis of Topological Derivative Based Localization of Small Electromagnetic Inclusions

Wahab

2015

SIAM J. Imaging Sci.

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The aim of this article is to elaborate and rigorously analyze a topological derivative based imaging framework for locating an electromagnetic inclusion of diminishing size from boundary measurements of the tangential component of scattered magnetic field at a fixed frequency. The inverse problem of inclusion detection is formulated as an optimization problem in terms of a filtered discrepancy functional and the topological derivative based imaging functional obtained therefrom. The sensitivity and resolution analysis of the imaging functional is rigorously performed. It is substantiated that the Rayleigh resolution limit is achieved. Further, the stability of the reconstruction with respect to measurement and medium noises is investigated and the signal-to-noise ratio is evaluated in terms of the imaginary part of free space fundamental magnetic solution.

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Topological derivative strategy for one-step iteration imaging of arbitrary shaped thin, curve-like electromagnetic inclusions

Cited by 49 publications

References 23 publications

Properties of Music-Type Algorithm for Imaging of Thin Dielectric Inhomogeneity in Limited-View Inverse Scattering Problem

Properties of Music-Type Algorithm for Imaging of Thin Dielectric Inhomogeneity in Limited-View Inverse Scattering Problem

Performance analysis of multi-frequency topological derivative for reconstructing perfectly conducting cracks

Stability and Resolution Analysis of Topological Derivative Based Localization of Small Electromagnetic Inclusions

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