On the convergence of a new Newton-type method in inverse scattering
On the convergence of a new Newton-type method in inverse scattering
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DOI：
10.1088/0266-5611/17/5/312
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发表时间：
2001-08
期刊：
影响因子：
2.1
通讯作者：
R. Potthast
中科院分区：
文献类型：
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作者：
R. Potthast
我们调查的重建域D从测量的远场图案散射的一些入射场ui，例如，为逆二维或三维声学软或二维电磁完美导体障碍物散射问题。研究了一个完美的牛顿格式、一个部分正则化的和一个完全正则化的带停止规则的牛顿格式。作为正则化方法，我们结合联合收割机准解决方案与点源方法，最小范数的解决方案，Tikhonov正则化或频谱截止。我们证明了超线性局部收敛的正则化牛顿更新的正则化的解决方案和收敛的正则化的解决方案向真正的解决方案时，数据误差趋于零，无论是在条件下，真正的解决方案有一个解析边界和正常的导数的总场没有零的边界上。此外，牛顿的方法的一个版本的点源方法的强关系时，牛顿更新被用来找到未知域从重建的散射场US。
We investigate the reconstruction of the domain D from the measured far field pattern for scattering of some incident field ui, e.g. for the inverse two- or three-dimensional acoustic sound-soft or two-dimensional electromagnetic perfect-conductor obstacle scattering problems. Both a perfect Newton scheme, a partially regularized and a fully regularized Newton scheme with stopping rule are investigated. As regularization methods we combine quasi-solutions with either the point-source method, minimum norm solutions, Tikhonov regularization or spectral cut-off. We prove superlinear local convergence of regularized Newton updates towards a regularized solution and the convergence of the regularized solution towards the true solution when the data error tends to zero, both under the condition that the true solution has an analytic boundary and the normal derivative of the total field has no zeros on the boundary. In addition, the strong relation of Newton's method to a version of the point-source method is shown when Newton updates are used to find the unknown domain from the reconstructed scattered field us.