A maximum product criterion as a Tikhonov parameter choice rule for Kirsch's factorization method

  • Authors:

  • FermíN S. V. BazáN;J. B. Francisco;Koung Hee Leem;G. Pelekanos

  • Affiliations:

  • Department of Mathematics, Federal University of Santa Catarina, Florianópolis SC, Santa Catarina, CEP 88040-900, Brazil;Department of Mathematics, Federal University of Santa Catarina, Florianópolis SC, Santa Catarina, CEP 88040-900, Brazil;Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, IL 62026, USA;Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, IL 62026, USA

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2012

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Abstract

Kirsch's factorization method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far-field pattern. We present a Tikhonov parameter choice approach based on a maximum product criterion (MPC) which provides a regularization parameter located in the concave part of the L-curve on a log-log scale. The performance of the method is evaluated by comparing our reconstructions with those obtained via the L-curve, Morozov's discrepancy principle and the SVD-tail. Numerical results that illustrate the effectiveness of the MPC in reconstruction problems involving both simulated and real data are reported and analyzed.