混合随机-确定性最小化方法在表面数据逆散射问题中的应用
Application of the hybrid stochastic-deterministic minimization method to a surface data inverse scattering problem
AI总结：
针对亥姆霍兹方程逆散射问题，提出一种混合随机-确定性最小化方法，通过全局最小化搜索识别小散射体的位置，并在Born近似失效时仍有效。
摘要：
在亥姆霍兹方程逆散射问题的框架下，提出了一种从表面数据识别小不均匀体的方法。利用散射体小的假设，将逆问题简化为识别小散射体的位置。这些位置通过全局最小化搜索找到，该搜索由一种新颖的混合随机-确定性最小化方法实现。该方法结合了随机尝试和确定性最小化。数值实验验证了该方法的有效性。在建模部分，我们的方法在Born近似失效时仍然有效。在数值部分，提出了一种估计小散射体数量的算法。
英文摘要：
A method for the identification of small inhomogeneities from a surface data is presented in the framework of an inverse scattering problem for the Helmholtz equation. Using the assumptions of smallness of the scatterers one reduces this inverse problem to an identification of the positions of the small scatterers. These positions are found by a global minimization search. Such a search is implemented by a novel Hybrid Stochastic-Deterministic Minimization method. The method combines random tries and a deterministic minimization. The effectiveness of this approach is illustrated by numerical experiments. In the modeling part our method is valid when the Born approximation fails. In the numerical part, an algorithm for the estimate of the number of the small scatterers is proposed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
