Adaptive refinement and selection process through defect localization for reconstructing an inhomogeneous refraction index

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

1 ONERA - The French Aerospace Lab [Toulouse]
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider the iterative reconstruction of both the internal geometry and the values of an inhomogeneous acoustic refraction index through a piecewise constant approximation. In this context, we propose two enhancements intended to reduce the number of parameters to reconstruct, while preserving accuracy. This is achieved through the use of geometrical informations obtained from a previously developed defect localization method. The first enhancement 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: inhomogeneous media; index reconstruction; Inverse scattering; defects localisation; factorisation method

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Yann Grisel, Vincent Mouysset, Pierre-Alain Mazet, Jean-Pierre Raymond. Adaptive refinement and selection process through defect localization for reconstructing an inhomogeneous refraction index. Inverse Problems, 2014, 30 (7), pp.5003. ⟨10.1088/0266-5611/30/7/075003⟩. ⟨hal-00814331v4⟩