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In inverse scattering problems, a model that allows for the simultaneousrecovery of both the domain shape and an impedance boundary condition covers awide range of problems with impenetrable domains, including recovering theshape of sound-hard and sound-soft obstacles and obstacles with thin coatings.This work develops an optimization framework for recovering the shape andmaterial parameters of a penetrable, dissipative obstacle in the multifrequencysetting, using a constrained class of curvature-dependent impedance functionmodels proposed by Antoine, Barucq, and Vernhet. We find that this constrainedmodel improves the robustness of the recovery problem, compared to more generalmodels, 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 numericalexamples.

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