数学
基础(线性代数)
积分方程
反问题
逆散射问题
数学分析
采样(信号处理)
边值问题
边界(拓扑)
反向
奇异积分
应用数学
计算机科学
几何学
计算机视觉
滤波器(信号处理)
作者
Fioralba Cakoni,David Colton
出处
期刊:Georgian Mathematical Journal
[De Gruyter]
日期:2003-09-01
卷期号:10 (3): 411-425
被引量:65
摘要
Abstract The linear sampling method is an algorithm for solving the inverse scattering problem for acoustic and electromagnetic waves. The method is based on showing that a linear integral equation of first kind has a solution that becomes unbounded as a parameter 𝑧 approaches the boundary of the scatterer 𝐷 from inside 𝐷. However, except for the case of the transmission problem, the case where z is in the exterior of 𝐷 is unresolved. Since for the inverse scattering problem 𝐷 is unknown, this step is crucial for the mathematical justification of the linear sampling method. In this paper we give a mathematical justification of the linear sampling method for arbitrary 𝑧 by using the theory of integral equations of first kind with singular kernels.
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