B样条函数在二维导体横截面轮廓成象中的应用

本文将B样条函数应用于根据多入射方向下的后散射场对二维导体柱横截面形状的反演,并将整个反演过程转化为两次非线性优化过程。由于两次优化的目标函数的导数都是可求得的,因此采用基于梯度的优化算法,如Broyden-Fletcher-Goldfard-Shanno变尺度算法(简称BFGS方法)。第一次优化最佳的等效圆柱的半径和深度,然后在第二次优化过程中再进一步优化导体柱横截面的控制节点以得到反演的形状。最后,以数值结果验证了该方法的有效性,并讨论了该方法的抗噪声性能。

APPLICATION OF B-SPLINE IN RECONSTRUCTION OF 2-D CONDUCTOR CROSS-SECTION

B-spline is applied to the reconstruction of 2-D conductor cross-section via backscat-tered field in near region illuminated by plane waves with different incident directions. The whole inverse problem may be viewed as a two-stage optimal procedure, and the optimal algorithm based on gradient, such as BFGS algorithm, is adopted as the gradient of the objective functions which may be derived by using Frechet differential. In the first step, the position and the radius of optimal circular cylinder are obtained, then in the second step, with above results as its initial values, the shape of 2-D cylinder can be reconstructed. The robustness of the proposed method is tested using different numerical results, and the effects of noise are discussed.