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Selection of defective components in unknown backgrounds

We shall present a new qualitative imaging method capable of identifying defects in unknown backgrounds from differential measures of farfield operators : i.e. far measurements of scattered waves in the configurations with and without defects. Indeed, the main difficulty is that the background physical properties and geometry are unknown. Our approach is based on a new exact characterization of a scatterer shape in terms of the far field operator range and the link with solutions to so-called interior transmission problems. We shall present the theoretical foundations of the method and some validating numerical experiments. The motivation behind this work is the identification of cracks in concrete like materials. Simulations of such configurations will also be discussed. This is a joint work with Lorenzo Audibert and Alexandre Girard.

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