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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Bibliographic Details
Published in:IEEE transactions on antennas and propagation Vol. 57; no. 4; pp. 1133 - 1149
Main Authors: De Zaeytijd, J., Franchois, A., Geffrin, J.-M.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.04.2009
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2009.2015823