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

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.