低频电磁场重建二维非均匀介质的有效方法

Efficient Approaches to Reconstructing Two-Dimensional Inhomogeneous Conductivity with Low-Frequency Electromagnetic Fields

将玻恩迭代和变形玻恩迭代两种方法用于低频二维非均匀介质电导率的重建。利用上述两种方法求解非线性积分方程。用正则化方法对解加上约束克服重建问题中解的非唯一性和不稳定性。数值计算表明，两种迭代方法都可用于二维非均匀介质电导率的重建。同玻恩迭代法相比，变形玻恩迭代法显示出更快的收敛性，而同变形玻恩迭代法相比，玻恩迭代法的抗噪声能力更强。

In this paper, two iterative methods for the Born iterative methed and the distorted Born iterative method are applied to the inversion of two-dimensional inhomogeneous conductivity for low-frequency. The nonlinear integral equation for unknown conductivity distribution is solved by us-ing the distorted Born iterative method and the forn iterative methods. The nonuniqueness and insta-bility of solutions in the inversion prob1em are circumvented by imposing additional constraints on the solution using the regularization. The numerical simulations show that two iterative metheds are both applied to the inversion of twodimensional inhomogeneous conductivity. The distorted Born iterative method displays faster convergence compared to the Born iterative method, while the Born iterative method is more robust to noise contamination compared to the distorted iterative method.