Identifying defects in an unknown background using differential measurements
Abstract
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 difficulty 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 far field 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.