Inverse Acoustic and Electromagnetic Scattering Theory

@inproceedings{Colton1992InverseAA,
  title={Inverse Acoustic and Electromagnetic Scattering Theory},
  author={David Colton and Rainer Kress},
  year={1992}
}
Introduction.- The Helmholtz Equation.- Direct Acoustic Obstacle Scattering.- III-Posed Problems.- Inverse Acoustic Obstacle Scattering.- The Maxwell Equations.- Inverse Electromagnetic Obstacle Scattering.- Acoustic Waves in an Inhomogeneous Medium.- Electromagnetic Waves in an Inhomogeneous Medium.- The Inverse Medium Problem.-References.- Index 
A point source method for inverse acoustic and electromagnetic obstacle scattering problems
We present the mathematical foundation for a point source method to solve some inverse acoustic and electromagnetic obstacle scattering problems in three dimensions. We investigate the inverse
The linear sampling method in inverse electromagnetic scattering theory
We survey the linear sampling method for solving the inverse scattering problem for time-harmonic electromagnetic waves at fixed frequency. We consider scattering by an obstacle as well as scattering
The linear sampling method in inverse electromagnetic scattering theory
We survey the linear sampling method for solving the inverse scattering problem for time-harmonic electromagnetic waves at fixed frequency. We consider scattering by an obstacle as well as scattering
On uniqueness in inverse acoustic and electromagnetic obstacle scattering problems
We review some of the uniqueness results in inverse acoustic and electromagnetic obstacle scattering problems. The emphasis is given to the recent progress on unique determination of general
Integral equation methods in electromagnetic scattering from anisotropic media
We investigate scattering of time-harmonic electromagnetic waves by an anisotropic inhomogeneous medium. The problem is equivalently transformed into a system of strongly singular integral equations.
An inverse electromagnetic scattering problem for a cavity
We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting cavity from measurement of the scattered electric field due to electric-dipole sources on
Nonlinear integral equations for an inverse electromagnetic scattering problem
We present a new method to solve an inverse scattering problem for time-harmonic electromagnetic waves. The method is based on an equivalence relation of the inverse problem to a system of two
Reflection principle for the Maxwell equations and its application to inverse electromagnetic scattering
A novel reflection principle for the time-harmonic Maxwell equations is established. It is then used to derive a uniqueness result in inverse electromagnetic obstacle scattering with polyhedral-type
Integral equation method for acoustic scattering by an inhomogeneous penetrable obstacle in a stratified medium
In this paper, we study the scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a stratified medium. By using the integral equation method, we prove the uniqueness
Scattering relations for point sources: Acoustic and electromagnetic waves
The problem of scattering of spherical waves by a bounded obstacle is considered. General scattering theorems are proved. These relate the far-field patterns due to scattering of waves from a point
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References

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On uniqueness in inverse obstacle scattering
The inverse problem we consider in this survey is to reconstruct the shape of an obstacle from the knowledge of the far field pattern for the scattering of time-harmonic acoustic or electromagnetic
An inverse transmission problem for the Helmholtz equation
The problem considered is that of determining the shape of a three-dimensional scattering object, illuminated by an acoustic field, from a knowledge of scattered far-field data. The far-field data
The domain derivative and two applications in inverse scattering theory
The author recalls the notion of the domain derivative of a functional. The existence and a characterization of the domain derivative of the far-field pattern for a scattering problem with Dirichlet
The interior transmission problem and inverse scattering from inhomogeneous media
This paper is concerned with the class of far field patterns corresponding to the scattering of time harmonic acoustic plane waves by an inhomogeneous medium in a bounded domain B, with refractive
On uniqueness in th invese transmission scattering problem
We give uniqueness results for the inverse scattering problem where the unknown scatterer D is a bounded open set and some coefficients of an elliptic equation are unknown as well. On the boundary of
Iterative method for multi-dimensional inverse scattering problems at fixed frequencies
Suppose that a medium with slowly changing spatial properties is enclosed in a bounded three-dimensional domain and is subjected to a scattering by plane waves of a fixed frequency. Let measurements
Inverse Problems in Partial Differential Equations
This workshop brought together mathematicians engaged in dif- ferent aspects of inverse problems for partial differential equations. Classical topics such as the inverse problems of impedance
Frechet differentiability of boundary integral operators in inverse acoustic scattering
Using integral equation methods to solve the time-harmonic acoustic scattering problem with Dirichlet boundary conditions, it is possible to reduce the solution of the scattering problem to the
Uniqueness Theorems for the Inverse Problem of Acoustic Scattering
On a obtenu des theoremes d'unicite pour le probleme de la determination de la forme d'un obstacle dur au son ou mou au son a partir de la connaissance du diagramme en champ lointain ou de la section
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