Identifying defects in an unknown background using differential measurements

Abstract

We present a new qualitative imaging method capable of selecting defects incomplex and unknown background from differential measurements of farfieldoperators: i.e. far measurements of scattered waves in the cases with andwithout defects. Indeed, the main difficulty is that the background physicalproperties are unknown. Our approach is based on a new exact characterizationof a scatterer domain in terms of the far field operator range and the linkwith solutions to so-called interior transmission problems. We present thetheoretical foundations of the method and some validating numerical experimentsin a two dimensional setting.