Inverse Acoustic and Electromagnetic Scattering Theory

Colton, David; Kreß, Rainer

doi:10.1007/978-3-662-02835-3

Cited by 2,125 publications

(3,837 citation statements)

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“…Furthermore, sinceẼ is a radiating solution to Maxwell's equations outside the domain bounded by , we conclude by the uniqueness of the scattering problem for a perfect conductor (c.f. [12]) thatẼ = 0 outside the domain bounded by . Then the unique continuation principle implies thatẼ = 0 outside D, whence both ν × W = 0 on D and…”

Section: Lemma 31 Assume That I Is Not Empty Then the Operator Rmentioning

confidence: 97%

“…TARGET IDENTIFICATION OF BURIED COATED OBJECTS After an appropriate scaling [12] and elimination of the magnetic field we now obtain the following equation for the electric field E in the background medium…”

Section: Formulation Of the Direct And Inverse Scattering Problemsmentioning

confidence: 99%

“…We remark that in what follows ν is always the outward unit normal to the surface under consideration unless otherwise stated. We remark that by modifying the approach in [12] it is possible to prove that the above data uniquely determines D and than the uniqueness for λ follows in the same way as in [16]. Here we are mainly concern with the solution of the inverse problem.…”

Section: Target Identification Of Buried Coated Objectsmentioning

confidence: 99%

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Target identification of buried coated objects

Cakoni¹,

Colton²

2006

Mat. apl. comput.

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Abstract.We consider the three dimensional electromagnetic inverse scattering problem of determining information about a buried coated object from a knowledge of the electric and magnetic fields measured on the surface of the earth corresponding to time harmonic electric dipoles as incident fields. We assume that the buried object is a perfect conductor that is (possibly) partially coated by a thin dielectric layer. No a priori assumption is made on the extent of the coating, i.e. the object can be fully coated, partially coated or not coated at all. We present an algorithm based on the linear sampling method and reciprocity gap functional for reconstructing the shape of the scattering obstacle together with an estimate of the surface impedance of the coating. Mathematical subject classification:

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Section: Lemma 31 Assume That I Is Not Empty Then the Operator Rmentioning

confidence: 97%

Section: Formulation Of the Direct And Inverse Scattering Problemsmentioning

confidence: 99%

Section: Target Identification Of Buried Coated Objectsmentioning

confidence: 99%

See 1 more Smart Citation

Target identification of buried coated objects

Cakoni¹,

Colton²

2006

Mat. apl. comput.

Self Cite

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“…solver with a finer discretization grid (N f wd = 51 × 51) to avoid the "inverse crime" [66]. With reference to a model-based representation of the scatterer, the descriptors at hand are here the value of the object function τ and the geometrical parameters of the cylinder, namely the radius ρ and the center coordinates (x c , y c ).…”

Section: Off-centered Homogeneous Circular Cylindermentioning

confidence: 99%

Microwave Imaging Within the Interval Analysis Framework

Rocca¹,

Carlin²,

Manica³

et al. 2013

PIER

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Abstract-An approach based on the use of the arithmetic of intervals and Interval Analysis for the solution of inverse scattering problems is presented and assessed. By exploiting the property of the Interval Analysis to find the global minimum of a functional in a n-dimensional space, the proposed approach adopts a branch and bound process to discard the regions of the solutions space not containing the global solution, while keeping those where a feasible solution is expected until a suitable converge criterion is reached. A representative set of results concerned with the reconstruction of circular dielectric objects within the first-order Born approximation are reported and discussed to show potentialities and current limitations of the proposed approach.

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“…Although intrinsic ill-posedness and nonlinearity of these problems appear consequentially in the inverse scattering problems [26][27][28][29], the study can be applied in widespread use. Most of the inversion techniques are investigated for the inverse problem using only single frequency scattering data (monochromatic source) [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Time Domain Inverse Scattering of a Two-Dimensional Homogenous Dielectric Object With Arbitrary Shape by Particle Swarm Optimization

Huang¹,

Chiu²,

Li³

et al. 2008

PIER

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Abstract-This paper presents a computational approach to the twodimensional time domain inverse scattering problem of a dielectric cylinder based on the finite difference time domain (FDTD) method and the particle swarm optimization (PSO) to determine the shape, location and permittivity of a dielectric cylinder. A pulse is incident upon a homogeneous dielectric cylinder with unknown shape and dielectric constant in free space and the scattered field is recorded outside. By using the scattered field, the shape and permittivity of the dielectric cylinder are reconstructed. The subgridding technique is implemented in the FDTD code for modeling the shape of the cylinder more closely. In order to describe an unknown cylinder with arbitrary shape more effectively, the shape function is expanded by closed cubicspline function instead of frequently used trigonometric series. The inverse problem is resolved by an optimization approach, and the global searching scheme PSO is then employed to search the parameter space. Numerical results demonstrate that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In addition, the effects of Gaussian noise on the reconstruction results are investigated. Numerical results show that even the measured scattered E fields are contaminated with some Gaussian noise, PSO can still yield good reconstructed quality.

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Inverse Acoustic and Electromagnetic Scattering Theory

Cited by 2,125 publications

References 0 publications

Target identification of buried coated objects

Target identification of buried coated objects

Microwave Imaging Within the Interval Analysis Framework

Time Domain Inverse Scattering of a Two-Dimensional Homogenous Dielectric Object With Arbitrary Shape by Particle Swarm Optimization

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