Fixed-point iterations in determining a Tikhonov regularization parameter in Kirsch’s factorization method

Kirsch’s factorization method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far-field pattern. The mathematical basis of this method is given by the far-field equation, which is a Fredholm integral equation of the first kind in which the data funct...

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Bibliographic Details
Published in:Applied mathematics and computation 2010-08, Vol.216 (12), p.3747-3753
Main Authors: Leem, Koung Hee, Pelekanos, George, Bazán, Fermín S. Viloche
Format: Article
Language:English
Subjects:
Computational efficiency
Corners
Factorization
Fixed points (mathematics)
Inverse scattering problems
Iterative methods
Kirch’s factorization method
L-curve criterion
Mathematical analysis
Mathematical models
Reconstruction
Regularization
Tikhonov regularization
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Summary:Kirsch’s factorization method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far-field pattern. The mathematical basis of this method is given by the far-field equation, which is a Fredholm integral equation of the first kind in which the data function is a known analytic function and the integral kernel is the measured (and therefore noisy) far-field pattern. We present a Tikhonov parameter choice approach based on a fast fixed-point iteration method which constructs a regularization parameter associated with the corner of the L-curve in log–log scale. The performance of the method is evaluated by comparing our reconstructions with those obtained via the L-curve and we conclude that our method yields reliable reconstructions at a lower computational cost.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.05.036