论文标题
最小二乘方法用于逆介质问题
Least-Squares Method for Inverse Medium Problems
论文作者
论文摘要
我们提出了一种两阶段最小二乘法，以从噪声数据同时重建多个未知系数的逆介质问题。采用直接采样方法来检测第一阶段不均匀性的位置，而使用混合正则化的总最小二乘方法用于在第二阶段恢复培养基。总体最小二乘法的设计旨在最大程度地减少模型方程的残差，以及数据拟合以及适当的正则化，以显着提高从第一阶段获得的近似值的准确性。我们还将提出有关该算法良好性和收敛性的分析。进行数值实验，以验证这种新型两阶段最小二乘算法的精度和鲁棒性，并具有很大的噪声。
We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the first stage, while a total least-squares method with mixed regularization is used to recover the medium profile in the second stage. The total least-squares method is designed to minimize the residual of the model equation and the data fitting, along with an appropriate regularization, in an attempt to significantly improve the accuracy of the approximation obtained from the first stage. We shall also present an analysis on the well-posedness and convergence of this algorithm. Numerical experiments are carried out to verify the accuracies and robustness of this novel two-stage least-squares algorithm, with great tolerance of noise.
