直接与逆散射中的优化方法
Optimization methods in direct and inverse scattering
AI总结：
本文综述了直接和逆散射问题中的多种参数拟合优化方法，包括混合随机-确定性最小化、稳定性指标法、修正瑞利猜想、支撑函数法和线性采样法，并讨论了理论和计算问题。
摘要：
在许多直接和逆散射问题中，由于解析反演方法通常不可用，必须使用参数拟合过程。本文介绍了多种此类方法，并讨论了理论和计算问题。通过混合随机-确定性最小化算法，从表面散射数据中寻找地下小夹杂物的问题得以解决。类似的方法用于从散射数据确定粒子中的层。描述了以固定能量相移为散射数据的球对称势的逆势散射问题，并通过稳定性指标法求解。该通用方法估计了最小化集合的大小，并为全局最小化算法提供了实际有用的停止准则。讨论了固定能量数据的3D逆散射问题及其通过Ramm方法的求解。通过修正瑞利猜想（MRC）方法处理障碍物直接散射问题。一种特殊的最小化过程允许廉价地计算具有光滑和非光滑表面的2D和3D障碍物的散射场。一种新的支撑函数法（SFM）用于逆障碍物散射问题。分析了另一种逆散射方法——线性采样法（LSM）。
英文摘要：
In many Direct and Inverse Scattering problems one has to use a parameter-fitting procedure, because analytical inversion procedures are often not available. In this paper a variety of such methods is presented with a discussion of theoretical and computational issues. The problem of finding small subsurface inclusions from surface scattering data is solved by the Hybrid Stochastic-Deterministic minimization algorithm. A similar approach is used to determine layers in a particle from the scattering data. The Inverse potential scattering problem for spherically symmetric potentials and fixed-energy phase shifts as the scattering data is described. It is solved by the Stability Index Method. This general approach estimates the size of the minimizing sets, and gives a practically useful stopping criterion for global minimization algorithms. The 3D inverse scattering problem with fixed-energy data and its solution by the Ramm's method are discussed. An Obstacle Direct Scattering problem is treated by a Modified Rayleigh Conjecture (MRC) method. A special minimization procedure allows one to inexpensively compute scattered fields for 2D and 3D obstacles having smooth as well as nonsmooth surfaces. A new Support Function Method (SFM) is used for Inverse Obstacle Scattering problems. Another method for Inverse scattering problems, the Linear Sampling Method (LSM), is analyzed.
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。
