A decoupling-based imaging method for inverse medium scattering for Maxwell's equations
Identifieur interne : 000462 ( Main/Exploration ); précédent : 000461; suivant : 000463A decoupling-based imaging method for inverse medium scattering for Maxwell's equations
Auteurs : A. Lakhal [Allemagne]Source :
- Inverse Problems [ 0266-5611 ] ; 2010.
English descriptors
- Teeft :
- Algorithm, Approximation, Axes unity, Boundary measurements, Cambridge university press, Complete orthonormal system, Computer tomography, Constitutive properties, Contrast function, Contrast source inversion method, Decoupling procedure, Differentiable functions, Einc, Eld, Electric contrast function, Electromagnetic, Electromagnetic imaging, Electromagnetic properties, Equivalent source, Experimental data, Frequency domain, Full linearization, Grid points, Habashy, Homogeneous background, Imaginary part, Imaging, Imaging method, Incident directions, Incident plane waves, Inhomogeneous media, Inner product, Inverse, Inverse medium, Inverse medium problem, Inverse problem, Inverse problems, Inverse source problem, Inversion, Iterative, Iterative method, Iterative reconstruction method, Iterative scheme, Kaczmarz, Kaczmarz algorithm, Kaczmarz iterations, Kaczmarz loop, Lakhal, Lakhal figure, Local nonlinear approximation, Localized, Localized nonlinear approximation, Ltered, Ltered version, Maxwell equations, Measurement operator, Medium properties, Multiple illuminations, Noisy data, Nonlinear, Object function, Propagation operator, Real part, Reconstruction algorithm, Reconstruction method, Relaxation parameter, Rytov approximation, Scalar, Singular functions, Singular value decomposition, Singular value expansion, Smooth boundary, Source operator, Spherical harmonics, Standard techniques, Synthetic data, Target region, Transmission eigenvalues, Uniqueness result.
Abstract
We present an iterative reconstruction method for an inverse medium scattering problem (IMP) for the three-dimensional time-harmonic Maxwell equations. The goal here is to determine the electromagnetic properties of a nonmagnetic unknown inhomogeneous object. The data are near-field measurements of scattered electric fields for multiple illuminations at a fixed frequency. We use the concept of the generalized induced source (GIS) to recast the intertwined vector equations of Maxwell into decoupled scalar scattering problems. To treat the nonlinearity of the IMP, we apply the localized nonlinear approximation due to Habashy and co-workers. In this framework, we derive a fast reconstruction method based on the Kaczmarz algorithm. Besides, for the underlying approximation we present a uniqueness result for determining the contrast function. Numerical experiments in 3D with synthetic and real data show the scope and limitations of the method.
Url:
DOI: 10.1088/0266-5611/26/1/015007
Affiliations:
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Lakhal</name><affiliation wicri:level="3"><country xml:lang="fr">Allemagne</country><wicri:regionArea>Institute of Applied Mathematics, Faculty of Mathematics and Computer Sciences, University of Saarland, D-66041 Saarbrcken</wicri:regionArea><placeName><region type="land" nuts="2">Sarre (Land)</region><settlement type="city">Sarrebruck</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Allemagne</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Inverse Problems</title><title level="j" type="abbrev">Inverse Problems</title><idno type="ISSN">0266-5611</idno><idno type="eISSN">1361-6420</idno><imprint><publisher>IOP Publishing</publisher><date type="published" when="2010">2010</date><biblScope unit="volume">26</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="1">1</biblScope><biblScope unit="page" to="17">17</biblScope><biblScope unit="production">Printed in the UK</biblScope></imprint><idno type="ISSN">0266-5611</idno></series><idno type="istex">3A3D81794C9A2894F1772FDA6CF6DCA0E6FD4D9F</idno><idno type="DOI">10.1088/0266-5611/26/1/015007</idno><idno type="PII">S0266-5611(10)31539-5</idno><idno type="articleID">331539</idno><idno type="articleNumber">015007</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0266-5611</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="Teeft" xml:lang="en"><term>Algorithm</term><term>Approximation</term><term>Axes unity</term><term>Boundary measurements</term><term>Cambridge university press</term><term>Complete orthonormal system</term><term>Computer tomography</term><term>Constitutive properties</term><term>Contrast function</term><term>Contrast source inversion method</term><term>Decoupling procedure</term><term>Differentiable functions</term><term>Einc</term><term>Eld</term><term>Electric contrast function</term><term>Electromagnetic</term><term>Electromagnetic imaging</term><term>Electromagnetic properties</term><term>Equivalent source</term><term>Experimental data</term><term>Frequency domain</term><term>Full linearization</term><term>Grid points</term><term>Habashy</term><term>Homogeneous background</term><term>Imaginary part</term><term>Imaging</term><term>Imaging method</term><term>Incident directions</term><term>Incident plane waves</term><term>Inhomogeneous media</term><term>Inner product</term><term>Inverse</term><term>Inverse medium</term><term>Inverse medium problem</term><term>Inverse problem</term><term>Inverse problems</term><term>Inverse source problem</term><term>Inversion</term><term>Iterative</term><term>Iterative method</term><term>Iterative reconstruction method</term><term>Iterative scheme</term><term>Kaczmarz</term><term>Kaczmarz algorithm</term><term>Kaczmarz iterations</term><term>Kaczmarz loop</term><term>Lakhal</term><term>Lakhal figure</term><term>Local nonlinear approximation</term><term>Localized</term><term>Localized nonlinear approximation</term><term>Ltered</term><term>Ltered version</term><term>Maxwell equations</term><term>Measurement operator</term><term>Medium properties</term><term>Multiple illuminations</term><term>Noisy data</term><term>Nonlinear</term><term>Object function</term><term>Propagation operator</term><term>Real part</term><term>Reconstruction algorithm</term><term>Reconstruction method</term><term>Relaxation parameter</term><term>Rytov approximation</term><term>Scalar</term><term>Singular functions</term><term>Singular value decomposition</term><term>Singular value expansion</term><term>Smooth boundary</term><term>Source operator</term><term>Spherical harmonics</term><term>Standard techniques</term><term>Synthetic data</term><term>Target region</term><term>Transmission eigenvalues</term><term>Uniqueness result</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract">We present an iterative reconstruction method for an inverse medium scattering problem (IMP) for the three-dimensional time-harmonic Maxwell equations. The goal here is to determine the electromagnetic properties of a nonmagnetic unknown inhomogeneous object. The data are near-field measurements of scattered electric fields for multiple illuminations at a fixed frequency. We use the concept of the generalized induced source (GIS) to recast the intertwined vector equations of Maxwell into decoupled scalar scattering problems. To treat the nonlinearity of the IMP, we apply the localized nonlinear approximation due to Habashy and co-workers. In this framework, we derive a fast reconstruction method based on the Kaczmarz algorithm. Besides, for the underlying approximation we present a uniqueness result for determining the contrast function. Numerical experiments in 3D with synthetic and real data show the scope and limitations of the method.</div></front></TEI><affiliations><list><country><li>Allemagne</li></country><region><li>Sarre (Land)</li></region><settlement><li>Sarrebruck</li></settlement></list><tree><country name="Allemagne"><region name="Sarre (Land)"><name sortKey="Lakhal, A" sort="Lakhal, A" uniqKey="Lakhal A" first="A" last="Lakhal">A. Lakhal</name></region><name sortKey="Lakhal, A" sort="Lakhal, A" uniqKey="Lakhal A" first="A" last="Lakhal">A. Lakhal</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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