Enhancement of a Gauss-Newton reconstruction for an inhomogeneous refraction index through defects localization

Yann Grisel (1, 2) , Jean-Pierre Raymond (3) , Pierre-Alain Mazet (1) , Vincent Mouysset (1)

1 ONERA - The French Aerospace Lab [Toulouse]
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 MIP - Mathématiques pour l'Industrie et la Physique

This paper deals with the reconstruction of both the internal geometry and the values of an inhomogenous acoustic refraction index through a piece-wise constant iterative approximation. We propose to enhance a classical Gauss-Newton scheme through the use of geometrical informations gained from a previously developed defects localization method. Both enhancements are aimed to reducing the number of computed parameters. The first one consists in a preliminary selection of relevant parameters, while the second one is an adaptive refinement to enhance precision with a low number of parameters. Each of them is numerically illustrated.

Mots clés: Inverse scattering; index reconstruction; inhomogeneous media; defects localisation; factorisation method

Domaines: Analyse numérique [math.NA]

Yann Grisel, Jean-Pierre Raymond, Pierre-Alain Mazet, Vincent Mouysset. Enhancement of a Gauss-Newton reconstruction for an inhomogeneous refraction index through defects localization. 2013. ⟨hal-00814331v2⟩