Discovery of point sources in the Helmholtz equation posed in unknown domains with obstacles
Discovery of point sources in the Helmholtz equation posed in unknown domains with obstacles
复制标题
发现有障碍物的未知域中亥姆霍兹方程中的点源
DOI：
10.4310/cms.2011.v9.n3.a11
复制
发表时间：
2011
影响因子：
1
通讯作者：
R. Tsai
中科院分区：
文献类型：
--
作者：
Y. Landa;N. Tanushev;R. Tsai
我们考虑了Helmholtz方程在可能存在未知障碍物的区域中的反源问题，这些障碍物比波长大得多。反问题是基于波场的稀疏测量来确定域中点源的数量和位置。我们提出的策略依赖于解决一个局部逆散射问题，以获得通过观测位置的波的入射方向。我们制定的问题作为一个L1约束最小化问题，并解决它使用Bregman迭代过程。然后追溯波方向射线，并且在来自几个观察位置的射线的交叉点处唯一地确定源。我们在2D中给出了示例，但是所有使用的公式和方法在3D中都有直接的类似物。
We consider an inverse source problem for the Helmholtz equation in domains with possibly unknown obstacles, which are much larger than the wavelength. The inverse problem is to determine the number and locations of point sources in the domain based on sparse measurements of the wave field. Our proposed strategy relies on solving a local inverse scattering problem to obtain the incoming directions of waves passing through an observation location. We formulate the problem as an L 1 constrained minimization problem and solve it using the Bregman iterative procedure. The wave direction rays are then traced back and sources are uniquely determined at the intersection of the rays from several observing locations. We present examples in 2D, however all of the formulas and methods used have direct analogues in 3D.