Differential Imaging of Local Perturbations in Anisotropic Periodic Media
For researchers in inverse scattering and imaging, this work incrementally extends a known method from isotropic to anisotropic periodic media.
The paper extends the differential sampling method to image local perturbations in anisotropic periodic media, proving Fredholm properties for the associated interior transmission problem and validating the approach with 2D numerical experiments using synthetic data.
We discuss the use of differential sampling method to image local perturbations in anisotropic periodic layers, extending earlier works on the isotropic case. We study in particular the new interior transmission problem that is associated with the inverse problem when only a single Floquet-Bloch mode is used. We prove Fredholm properties of this problem under similar assumptions as for classical interior transmission problems. The result of the analysis is then exploited to design an indicator function for the local perturbation. The resulting numerical algorithm is validated for two dimensional numerical experiments with synthetic data.