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.

翻译：在逆散射问题中，允许同时恢复区域形状和阻抗边界条件的模型涵盖了广泛的不穿透区域问题，包括恢复硬声障碍物、软声障碍物以及薄涂层障碍物的形状。本文针对多频设置下的可穿透耗散障碍物，提出一种基于Antoine、Barucq和Vernhet提出的曲率相关阻抗函数模型约束类的优化框架，用于恢复其形状与材料参数。研究发现，与更通用的模型相比，该约束模型能提升恢复问题的鲁棒性，并且比简单模型实现更有意义的障碍物恢复。数值算例中，我们考察了该模型在不同耗散程度、含噪数据及有限孔径数据条件下的有效性。