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Kirsch, A. (1998) Characterization of the Shape of the Scattering Obstacle by the Spectral Data of the Far-Field Operator. Inverse Problems, 14, 1489-1512.
https://doi.org/10.1088/0266-5611/14/6/009

has been cited by the following article:

• TITLE: On an Application of the Improved Maximum Product Criterion to Inverse Acoustic Scattering in a Layered Medium

  AUTHORS: Fermin S. Viloche Bazán, Juliano de Bem Francisco, Koung Hee Leem, George Pelekanos, Vassilios Sevroglou

  KEYWORDS: Acoustic Scattering, Layered Medium, Mixed Reciprocity Relation, Factorization Method, Improved Maximum Product Criterion (IMPC)

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.9 No.4, April 21, 2021

  ABSTRACT: In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well known factorization method, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a mixed reciprocity principle, which renders the computation of the Green function at the background medium unnecessary. Moreover, to further refine our inversion algorithm, an efficient Tikhonov parameter choice technique, called Improved Maximum Product Criterion (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no a priori knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.