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The linear sampling method for anisotropic media
, 2002
"... We consider the inverse scattering problem of determining the support of an anisotropic inhomogeneous medium from a knowledge of the incident and scattered time harmonic acoustic wave at fixed frequency. To this end, we extend the linear sampling method from the isotropic case to the case of anisotr ..."
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Cited by 37 (19 self)
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We consider the inverse scattering problem of determining the support of an anisotropic inhomogeneous medium from a knowledge of the incident and scattered time harmonic acoustic wave at fixed frequency. To this end, we extend the linear sampling method from the isotropic case to the case of anisotropic medium. In the case when the coefficients are real we also show that the set of transmission eigenvalues forms a discrete set.
The Linear Sampling Method For Solving The Electromagnetic Inverse Scattering Problem
"... We consider the inverse scattering problem of determining the shape of an obstacle in R³ from a knowledge of the time harmonic incident electromagnetic wave and the far eld pattern of the scattered wave with frequency in the resonance region. The approach used is the linear sampling method which doe ..."
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Cited by 22 (9 self)
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We consider the inverse scattering problem of determining the shape of an obstacle in R³ from a knowledge of the time harmonic incident electromagnetic wave and the far eld pattern of the scattered wave with frequency in the resonance region. The approach used is the linear sampling method which does not require a priori knowledge of either the boundary condition or the connectivity of the scattering obstacle. Numerical examples are given for the case of both a simply connected perfect conductor and multiply connected obstacles satisfying an impedance boundary condition on the boundary of the one component and a perfect conducting boundary condition on the boundary of another component.
The computation of lower bounds for the norm of the index of refraction in an anisotropic media from far field data
 Jour. Integral Equations and Applications
"... Dedicated to Professor Dr. Rainer Kress on the occasion of his 65th birthday and the pleasure that knowing him has given to our lives! ABSTRACT. We consider the scattering of time harmonic electromagnetic plane waves by a bounded, inhomogeneous, anisotropic dielectric medium and show that under cert ..."
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Cited by 19 (8 self)
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Dedicated to Professor Dr. Rainer Kress on the occasion of his 65th birthday and the pleasure that knowing him has given to our lives! ABSTRACT. We consider the scattering of time harmonic electromagnetic plane waves by a bounded, inhomogeneous, anisotropic dielectric medium and show that under certain assumptions a lower bound on the norm of the (matrix) index of refraction can be obtained from a knowledge of the smallest transmission eigenvalue corresponding to the medium. Numerical examples are given showing the efficaciousness of our estimates. 1. Introduction. Anisotropic
A Regularized Sampling Method for Solving Three Dimensional Inverse Scattering Problems
 SIAM J. Sci. Comput
, 2000
"... The inverse scattering problem under consideration is to determine the shape of an obstacle in R³ from a knowledge of the time harmonic incident acoustic wave and the far field pattern of the scattered wave with frequency in the resonance region. A method for solving this nonlinear and impr ..."
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Cited by 16 (2 self)
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The inverse scattering problem under consideration is to determine the shape of an obstacle in R&sup3; from a knowledge of the time harmonic incident acoustic wave and the far field pattern of the scattered wave with frequency in the resonance region. A method for solving this nonlinear and improperly posed problem is presented which is based on solving a linear integral equation of the first kind and avoids the use of nonlinear optimization methods. Numerical examples are given showing the practicality of this new approach.
ThreeDimensional Electromagnetic Inverse Scattering by Local Shape Function Method with CGFFT
"... A numerical algorithm for the reconstruction of the permittivity of a threedimensional penetrable object from scattering data is presented. The reconstruction algorithm is based on the local shape function method (LSF) combined with the conjugate gradient method with FFT (CGFFT). The nonlinearity du ..."
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Cited by 7 (0 self)
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A numerical algorithm for the reconstruction of the permittivity of a threedimensional penetrable object from scattering data is presented. The reconstruction algorithm is based on the local shape function method (LSF) combined with the conjugate gradient method with FFT (CGFFT). The nonlinearity due to the multiple scattering is accounted for in an iterative minimization scheme. Numerical examples of simulation data are given showing the capability of this algorithm. 1. Introduction The use of scattered electromagnetic waves to determine the parameters of unknown objects is a muchstudied problem in the fields of remote sensing, nondestructive evaluation, and medical imaging. These parameters could be the location, shape and size of a metallic body [1][8]; the permittivity of a penetrable object [9] [16]; the conductivity of underground for welllogging [17][19]; or the soil moisture, trunk and leaf density for remote sensing [20]. Thus far, linearizations obtained by the firstor...
Anisotropic inverse conductivity and scattering problems
 Inverse Problems 18
, 2002
"... Uniqueness in inverse conductivity and scattering problems is considered. In case the medium consists of two discontinuous constant anisotropic conductive parts, the measurements of potential and induced currents on the boundary of surrounding body are enough to guarantee uniqueness to determine con ..."
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Cited by 4 (2 self)
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Uniqueness in inverse conductivity and scattering problems is considered. In case the medium consists of two discontinuous constant anisotropic conductive parts, the measurements of potential and induced currents on the boundary of surrounding body are enough to guarantee uniqueness to determine conductivity and region of embedded unknown material under a very weak condition. The analogous uniqueness result is also obtained for an inverse scattering problem in the case that the medium is composed of two anisotropic and homogeneous materials. Key words: anisotropic medium, inverse problem, conductivity, scattering 1
Inequalities in Inverse Scattering Theory
 J. of Inverse and Illposed Problems
"... Abstract. We consider the scattering of time harmonic electromagnetic plane waves by a bounded, inhomogeneous dielectric medium that is partially coated by a thin metallic layer in R 2. We use far field pattern of the scattered waves at a fixed frequency as data to determine the support D of the inh ..."
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Cited by 1 (1 self)
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Abstract. We consider the scattering of time harmonic electromagnetic plane waves by a bounded, inhomogeneous dielectric medium that is partially coated by a thin metallic layer in R 2. We use far field pattern of the scattered waves at a fixed frequency as data to determine the support D of the inhomogeneous obstacle, the surface conductivity that characterizes the coating and the relative permittivity. No a prior information on the material properties of the scatterer is needed. The support D is determined by the linear sampling method which is based on the approximate solution of the far field equation. This solution is also used to obtain lower bounds for the surface conductivity and relative permittivity. The techniques for solving this inverse scattering problem rely on the analysis of a non standard boundary value problem known as the interior transmission problem. Key words. Inverse scattering problem, inhomogeneous medium, interior transmission problem, electromagnetic waves, mixed boundary value problems, qualitative approaches in inverse scattering. AMS classification. 35P25, 35R30, 78A45. 1.
High Contrast Microwave Tomography using Topology Optimization Techniques
"... The preprint agrees with published version,. Microwave tomography for medical applications leads to a difficult reconstruction problem for the dielectric properties of biological tissue due to strongly diffracting waves in combination with large dielectric contrasts. We apply the material distribut ..."
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The preprint agrees with published version,. Microwave tomography for medical applications leads to a difficult reconstruction problem for the dielectric properties of biological tissue due to strongly diffracting waves in combination with large dielectric contrasts. We apply the material distribution technique used for topology optimization of elastic structures in order to solve the nonlinear leastsquares problem underlying the reconstruction problem. Using simulated numerical data with an approximate signaltonoise ratio of 40 dB and geometrical a priori information on the unknown objects, we obtain good estimates of the dielectric properties corresponding to biological objects.