论文标题
关于具有复杂边界的可穿透性，均匀物体的反向散射的稳健性
On the robustness of inverse scattering for penetrable, homogeneous objects with complicated boundary
论文作者
论文摘要
声学逆障碍物散射问题包括由于某些入射场（探针）而从散射远场的测量中确定域的形状。对于具有已知声速的可穿透对象，可以通过将边界视为未知曲线来实现。另外，人们可以将整个对象视为未知的对象，并使用更通用的体积表示，而无需使用已知的音速。两者都导致强烈的非线性和非凸优化问题，递归线性化为数值分析提供了有用的框架。在扩展了针对不可穿透身体的早期开发的形状优化方法之后，我们对这两种方法进行了系统的研究，并在各种示例中比较了它们的性能。我们的发现表明，尽管自由度的数量明显更大，但体积方法也更强大。最后，我们讨论了这种现象和进一步研究的潜在方向。
The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (probes). For a penetrable object with known sound speed, this can be accomplished by treating the boundary alone as an unknown curve. Alternatively, one can treat the entire object as unknown and use a more general volumetric representation, without making use of the known sound speed. Both lead to strongly nonlinear and nonconvex optimization problems for which recursive linearization provides a useful framework for numerical analysis. After extending our shape optimization approach developed earlier for impenetrable bodies, we carry out a systematic study of both methods and compare their performance on a variety of examples. Our findings indicate that the volumetric approach is more robust, even though the number of degrees of freedom is significantly larger. We conclude with a discussion of this phenomenon and potential directions for further research.
