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 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 than the L-curve. Keywords Inverse scattering problems, Kirch's factorization method, Tikhonov regularization, L-curve criterion.

• Type: Journal
• Year: 2010
• Where: AMC
• Authors: Koung Hee Leem, George Pelekanos, Fermín S. Viloche Bazán
• Keywords: AMC 2010, Factorization Method, Fast Inversion Technique, Fredholm Integral Equation