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引用次数: 0
摘要
在反向散射问题中,允许同时恢复领域形状和阻抗边界条件的模型涵盖了具有不可穿透领域的各种问题,包括恢复声硬和声软障碍物以及具有薄涂层的障碍物的形状。本研究利用 Antoine 等人提出的一类受约束的曲率依赖阻抗函数模型(2001 Asymptotic Anal.26,257-83),建立了一个优化框架,用于在多频环境下恢复可穿透耗散障碍物的形状和材料参数。我们发现,在某些情况下,与更一般的模型相比,这种约束模型提高了恢复问题的鲁棒性,与更简单的模型相比,障碍物恢复效果更好。我们在数值示例中探讨了该模型对不同程度的耗散、噪声干扰数据和有限孔径数据的有效性。
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 et al (2001 Asymptotic Anal.26 257–83). We find that in certain regimes 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.