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

作　　者：Fermin S. Viloche Bazán Juliano de Bem Francisco Koung Hee Leem George Pelekanos Vassilios Sevroglou Fermin S. Viloche Bazán;Juliano de Bem Francisco;Koung Hee Leem;George Pelekanos;Vassilios Sevroglou(Department of Mathematics, Federal University of Santa Catarina, Florianopolis SC, Santa Catarina, Brazil;Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, USA;Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece)

机构地区：[1]Department of Mathematics, Federal University of Santa Catarina, Florianopolis SC, Santa Catarina, Brazil [2]Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, USA [3]Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece

出　　处：《Journal of Applied Mathematics and Physics》2021年第4期661-682,共22页应用数学与应用物理（英文）

摘　　要：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 <em>factorization method</em>, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a <em>mixed reciprocity principle</em>, 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 <em>Improved Maximum Product Criterion</em> (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no <em>a priori</em> knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.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 <em>factorization method</em>, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a <em>mixed reciprocity principle</em>, 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 <em>Improved Maximum Product Criterion</em> (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no <em>a priori</em> knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.

关 键 词：Acoustic Scattering Layered Medium Mixed Reciprocity Relation Factorization Method Improved Maximum Product Criterion (IMPC) 

分 类 号：O17[理学—数学]