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首页> 外文期刊>Journal of inverse and ill-posed problems >A second order Newton method for sound soft inverse obstacle scattering
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A second order Newton method for sound soft inverse obstacle scattering

机译：声软逆障碍物散射的二阶牛顿法

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摘要

A new second order Newton method for reconstructing the shape of a sound soft scatterer from the measured far-field pattern for scattering of time harmonic plane waves is presented. This method extends a hybrid between regularized Newton iterations and decomposition methods that has been suggested and analyzed in a number of papers by Kress and Serranho [11-13, 16, 17] and has some features in common with the second degree method for ill-posed nonlinear problems as considered by Hettlich and Rundell [8]. The main idea of our iterative method is to use Huygen's principle, i.e., represent the scattered field as a single-layer potential. Given an approximation for the boundary of the scatterer, this leads to an ill-posed integral equation of the first kind that is solved via Tikhonov regularization. Then, in a second order Taylor expansion, the sound soft boundary condition is employed to update the boundary approximation. In an iterative procedure, these two steps are alternated until some stopping criterium is satisfied. We describe the method in detail and illustrate its feasibility through examples with exact and noisy data.
机译：提出了一种新的二阶牛顿法，用于从测得的远场模式中重建声软散射体的形状，以散射时间谐波平面波。这种方法扩展了正则化牛顿迭代和分解方法之间的混合，Kress和Serranho [11-13，16，17]在许多论文中已经提出和分析了混合方法，并且与不适度的二阶方法具有一些共同点。由Hettlich和Rundell [8]提出的非线性问题。我们的迭代方法的主要思想是使用惠更斯原理，即将散射场表示为单层电势。给定散射体的边界的近似值，这将导致第一类不适定积分方程，该方程可通过Tikhonov正则化求解。然后，在二阶泰勒展开中，采用声音软边界条件来更新边界近似。在迭代过程中，将这两个步骤交替进行，直到满足一些停止条件为止。我们将详细描述该方法，并通过带有准确和嘈杂数据的示例说明其可行性。

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