Imaging of anomalous components in unknown background

Lorenzo Audibert (1, 2) , Alexandre Girard (1) , Haddar Houssem (2)

1 EDF R&D STEP - Simulation et Traitement de l'information pour l'Exploitation des systèmes de Production
2 DeFI - Shape reconstruction and identification

We introduce a qualitative method capable of imaging defects in an unknown complex environment using differential measurements. The main difficulty is that the back-ground medium is unknown and too complex to obtain a reliable estimate of the associated Green function. To overcome this difficulty our approach exploits two measurements of the farfield operators, one without defects and one with defects. The analysis of our method relies on the recently introduced Generalized Linear Sampling Methods (GLSM) and the link to the solutions of the interior transmission problems. We give numerical examples related to non destructive testing in concrete-like materials, illustrating the performance of our method.

Mots clés: Inverse scattering; Sampling methods; differential measurement

Domaines: Analyse numérique [cs.NA]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Physique mathématique [math-ph]; Sciences de l'ingénieur [physics]; Informatique [cs]

Lorenzo Audibert, Alexandre Girard, Haddar Houssem. Imaging of anomalous components in unknown background. Inverse Problems from Theory to Application, Aug 2014, Bristol, United Kingdom. ⟨hal-01111866⟩