论文标题
3D反向散射问题的凸化和实验数据与移动点源
Convexification and experimental data for a 3D inverse scattering problem with the moving point source
论文作者
论文摘要
边界测量中介质物理性质重建的反向散射问题实质上具有挑战性。这项工作旨在验证针对埋在沙盒中的对象的情况下，用于3D系数反问题的新开发的凸化方法的实验数据的性能，固定频率和点源沿直线的间隔移动。使用特殊的傅立叶基础，这项工作的方法强烈依赖于耦合的准椭圆方程系统的边界价值问题的新推导。反过来，通过最小化Tikhonov的功能，该问题是通过Carleman重量函数加权的。数值程序的全局收敛性是通过分析建立的。数值验证是使用实验数据进行的，这些数据是电场的原始反向散射数据。这些数据是使用北卡罗来纳大学夏洛特大学的微波散射设施收集的。
Inverse scattering problems of the reconstructions of physical properties of a medium from boundary measurements are substantially challenging ones. This work aims to verify the performance on experimental data of a newly developed convexification method for a 3D coefficient inverse problem for the case of objects buried in a sandbox a fixed frequency and the point source moving along an interval of a straight line. Using a special Fourier basis, the method of this work strongly relies on a new derivation of a boundary value problem for a system of coupled quasilinear elliptic equations. This problem, in turn, is solved via the minimization of a Tikhonov-like functional weighted by a Carleman Weight Function. The global convergence of the numerical procedure is established analytically. The numerical verification is performed using experimental data, which are raw backscatter data of the electric field. These data were collected using a microwave scattering facility at The University of North Carolina at Charlotte.
