A New Value Picking Regularization Strategy-Application to the 3-D Electromagnetic Inverse Scattering Problem

The nonlinear electromagnetic inverse scattering problem of reconstructing a possibly quasi-piecewise constant inhomogeneous complex permittivity profile is solved by iterative minimization of a pixel-based data fit cost function. Because of the ill-posedness it is necessary to introduce some form o...

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Veröffentlicht in:	IEEE transactions on antennas and propagation Jg. 57; H. 4; S. 1133 - 1149
Hauptverfasser:	De Zaeytijd, J., Franchois, A., Geffrin, J.-M.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York, NY IEEE 01.04.2009 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Applied classical electromagnetism Applied sciences Cost function Degradation Diffraction, scattering, reflection Electromagnetic scattering Electromagnetic wave propagation, radiowave propagation Electromagnetism Electromagnetism; electron and ion optics Engineering Sciences Exact sciences and technology Fundamental areas of phenomenology (including applications) Inverse problems Least squares methods microwave imaging Newton method optimization methods Optimization techniques Permittivity Physics Radiocommunications Radiowave propagation Recursive estimation regularization Smoothing methods Studies Telecommunications Telecommunications and information theory Testing Electromagnetic wave scattering Cost minimization Picking Inverse scattering method Piecewise constant techniques regularization Updating Iterative method Inverse scattering problem optimization methods Optimization Inverse problem Electromagnetic wave propagation Electromagnetic scattering Wave scattering inverse problems A priori estimation Cost function Complex permittivity Permittivity Microwave imaging
ISSN:	0018-926X, 1558-2221
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Zusammenfassung:	The nonlinear electromagnetic inverse scattering problem of reconstructing a possibly quasi-piecewise constant inhomogeneous complex permittivity profile is solved by iterative minimization of a pixel-based data fit cost function. Because of the ill-posedness it is necessary to introduce some form of regularization. Many authors apply a smoothing constraint on the reconstructed permittivity profile, but such regularization smooths away sharp edges. In this paper, a simple yet effective regularization strategy, the value picking (VP) regularization, is proposed. This new technique is capable of reconstructing piecewise constant permittivity profiles without degrading the edges. It is based on the knowledge that only a few different permittivity values occur in such profiles, the values of which need not be known in advance. VP regularization does not impose this a priori information in a strict sense, such that it can be applied also to profiles that are only approximately piecewise constant. The VP regularization is introduced in the solution of the inverse problem by adding a choice function to the data fit cost function for every permittivity unknown in the discretized problem. When minimized, the choice function forces the corresponding permittivity unknown to be close to one member of a set of auxiliary variables, the VP values, which are continuously updated throughout the iterations. To minimize the regularized cost function, a half quadratic Gauss-Newton optimization technique is presented. Finally, a stepwise relaxed VP regularization scheme is proposed, in which the number of VP values is gradually increased. This scheme is tested with synthetic and measured scattering data, obtained from inhomogeneous 3D targets, and is shown to achieve high reconstruction quality.
Bibliographie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
ISSN:	0018-926X 1558-2221
DOI:	10.1109/TAP.2009.2015823