Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume

Ammari, Habib; Moskow, Shari; Vogelius, Michael

doi:10.1051/cocv:2002071

Cited by 82 publications

(103 citation statements)

References 15 publications

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“…The method of reconstruction we propose here consists, as in [5], of sampling values of Λ α (η) at some discrete set of points and then calculating the corresponding discrete inverse Fourier transform. After a rescaling by − 1 2 , the support of this discrete inverse Fourier transform yields the location of the small imperfections B α .…”

Section: Remark 22mentioning

confidence: 99%

“…The determination of conductivity profiles from knowledge of boundary measurements has received a great deal of attention (see, for example, [1,2,5,20,32]). However, the reconstruction of imperfections within a dynamical (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…The inverse problem considered in this paper is more complicated from the mathematical point of view and more interesting from the point of view of applications than the one solved in [5,32] because one often cannot get measurements for all t or on the whole boundary, and so one cannot, by taking a Fourier transform in the time variable, reduce our dynamic inverse problem to the Helmholtz equation considered in [5,32]. Previous numerical investigations have concentrated on time independent equations with full data -see for example, [6,7,12].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume

Asch¹,

Darbas²,

Duval³

2010

ESAIM: COCV

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Abstract.We consider the numerical solution, in two-and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of "limited-view" data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for localizing the centers of the imperfections. Numerical results, in 2-and 3-D, show the robustness and accuracy of the approach for retrieving randomly placed imperfections from both complete and partial boundary measurements.Mathematics Subject Classification. 35R30, 35L05, 65M60.

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Section: Remark 22mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume

Asch¹,

Darbas²,

Duval³

2010

ESAIM: COCV

View full text Add to dashboard Cite

show abstract

“…Conversely, certain non-iterative shape reconstruction algorithms have been proposed; for example, MUltiple SIgnal Classification (MUSIC) algorithm [6,10,32,34], linear sampling method [15,21], Kirchhoff migration [6,28,29,33], and Fourier inversion based one [8,9,11]. In contrast with the iterative strategy, these algorithms require a large amount of incident field data and a significant number of boundary measurements.…”

Section: Introductionmentioning

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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“…The asymptotic formulas for diametrically small conductivity inhomogeneities and scatterers known so far form the foundation of several efficient reconstruction methods for inverse conductivity problems (see, e.g., Ammari, Moskow, and Vogelius [7], Ammari and Seo [8] or Brühl, Hanke, and Vogelius [17]) and inverse scattering problems for Maxwell's equations (see, e.g., Ammari et al [2], Iakovleva et al [33], Volkov [42], or [28,29,31,32]). In addition the general formula for electrostatic potentials from [18] has recently been used to investigate inverse conductivity problems for wires and tubes (see Beretta et al [13] or [30]).…”

Section: Introductionmentioning

confidence: 99%

A general perturbation formula for electromagnetic fields in presence of low volume scatterers

Griesmaier

2011

ESAIM: M2AN

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Abstract.In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This smallness typically causes problems when solving direct scattering problems due to the need to discretize the objects and also when solving inverse scattering problems because small objects have very little effect on electromagnetic fields. In this paper we consider an asymptotic representation formula for scattered electromagnetic waves caused by low volume objects contained in some otherwise homogeneous threedimensional bounded domain, assuming only that the scatterers are measurable and well-separated from the boundary of the domain. The formula yields a very general asymptotic model for electromagnetic scattering due to low volume objects that can either be used to simulate the corresponding electromagnetic fields or as the foundation of efficient reconstruction methods for inverse scattering problems with low volume scatterers.

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Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume

Cited by 82 publications

References 15 publications

Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume

Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume

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

A general perturbation formula for electromagnetic fields in presence of low volume scatterers

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