Identifying defects in an unknown background using differential measurements

We present a new qualitative imaging method capable of selecting defects in complex and unknown background from differential measurements of farfield operators: i.e. far measurements of scattered waves in the cases with and without defects. Indeed, the main diffculty is that the background physical properties are unknown. Our approach is based on a new exact characterization of a scatterer domain in terms of the farfield operator range and the link with solutions to so-called interior transmission problems. We present the theoretical foundations of the method and some validating numerical experiments in a two dimensional setting.