Reconstructing the shape and material parameters of dissipative obstacles using an impedance model

In inverse scattering problems, a model that allows for the simultaneous recovery of both the domain shape and an impedance boundary condition covers a wide range of problems with impenetrable domains, including recovering the shape of sound-hard and sound-soft obstacles and obstacles with thin coatings. This work develops an optimization framework for recovering the shape and material parameters of a penetrable, dissipative obstacle in the multifrequency setting, using a constrained class of curvature-dependent impedance function models proposed by Antoine, Barucq, and Vernhet. We find that this constrained model improves the robustness of the recovery problem, compared to more general models, and provides meaningfully better obstacle recovery than simpler models. We explore the effectiveness of the model for varying levels of dissipation, for noise-corrupted data, and for limited aperture data in the numerical examples.