Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration

Abstract

In this paper, the structure analysis of the direct sampling method (DSM) in the 3D electromagnetic inverse scattering problem in both near-field and far-field configurations is carried out. Even though the DSM is known to be a robust, fast, and efficient non-iterative type algorithm to estimate support and shape of unknown inhomogeneities from the knowledge of scattered data in the 2D scalar electromagnetic case, the choice of a proper test polarization dipole since the data are vectorial in the 3D vector case is to be dealt with, since indeed key to the success of 3D DSM. Here we carefully analyze the indicator function of DSM using the asymptotic formula of the scattered field under a small volume hypothesis of well-separated inhomogeneities. Thanks to it, an analytic formula of the 3D DSM indicator function is established. The already proposed heuristic method to choose the polarization test dipole is theoretically justified, and new methods developed for better efficiency. Numerical simulations from synthetic and experimental data validate the theoretical results.