Houssem Haddar

Preprocessing the Reciprocity Gap Sampling Method in Buried-Object Imaging Experiments

A reciprocity gap linear sampling method (RG-LSM) coupled with an analytic continuation method is proposed to localize and retrieve the shape of objects buried under a rough surface from multistatic data at a fixed frequency. The obtained procedure makes feasible the application of the RG-LSM algorithm to imaging experiments where the data are collected in the upper domain. It does not require the computation of the Greens function of the background layered medium and also does not require any a priori knowledge on the number or the physical properties of the buried scatterers. The efficiency and robustness of the method are validated through various numerical experiments for single and multiconnected objects.

Reconstruction of the Electromagnetic Field in Layered Media Using the Concept of Approximate Transmission Conditions

We propose a fast and stable method to reconstruct the electromagnetic field in layered media from overdetermined data on the outer boundary. This procedure can be used for instance as a data pre-processing in inversion algorithms to accurately image buried objects under known stratified structures. Our method is based on successive use of so-called approximate transmission conditions that provide accurate reconstructions for layers with sufficiently small width. The feasibility and efficiency of the proposed method are demonstrated by numerical experiments.