Imaging of local rough surfaces by the linear sampling method with near-field data
Imaging of local rough surfaces by the linear sampling method with near-field data
复制标题
利用近场数据的线性采样方法对局部粗糙表面进行成像
DOI：
10.1137/16m1097997
复制
发表时间：
2017
影响因子：
2.1
通讯作者：
杨家青
中科院分区：
文献类型：
--
作者：
丁萌;李建樑;刘可汲;杨家青
考虑时谐点源在无界粗糙面上的散射问题。假设曲面在有限区间上不同于平面曲面，使得模型问题可以转化为具有紧支撑边界数据的等价边值问题。因此，适定性证明采用变分方法与经典Fredholm理论。通过构造一个修正的近场方程，我们提出了一种新的采样型方法来重建局部粗糙表面的形状和位置，产生一个快速成像算法。数值实验表明了该方法的有效性。
Consider the scattering of a time-harmonic point source from an unbounded rough surface. The surface is assumed to be different from a plane surface over a finite interval, which leads to the situation that the model problem can be reduced to an equivalent boundary value problem with compactly supported boundary data. Well-posedness is thus proved by employing the variational method with classical Fredholm theory. By constructing a modified near-field equation, we then propose a novel sampling-type method for reconstructing the shape and location of the local rough surface, yielding a fast imaging algorithm. Numerical experiments are presented to illustrate the effectiveness of the method.