Inverse Source Problems for the Helmholtz Equation and the Windowed Fourier Transform II
Inverse Source Problems for the Helmholtz Equation and the Windowed Fourier Transform II
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DOI：
10.1137/130908658
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发表时间：
2013-09
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影响因子：
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通讯作者：
Roland Griesmaier;M. Hanke;T. Raasch
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文献类型：
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作者：
Roland Griesmaier;M. Hanke;T. Raasch
在这项工作中，我们扩展了最近在[R。Griesmaier，M. Hanke和T. Raasch，SIAM J. Sci.计算：34（2012），pp. A1544-A1562]，以相关的三维设置。重建算法依赖于这样一个事实，即一个窗口的傅里叶变换的远场图案的辐射波的compulsible支持源近似的指数射线变换与一个纯粹的虚指数的一个软化版本的源。一个过滤的反投影方案的标准射线变换应用于窗口傅立叶变换的远场图案的绝对值被用来恢复信息的支持源。我们提供的方法的理论基础，讨论了全三维算法的数值实现，并提出了一系列的数值例子，包括逆散射问题，以S…
In this work we extend the qualitative reconstruction method for inverse source problems for time-harmonic acoustic and electromagnetic waves in free space, recently developed in [R. Griesmaier, M. Hanke, and T. Raasch, SIAM J. Sci. Comput., 34 (2012), pp. A1544--A1562], to a relevant three-dimensional setting. The reconstruction algorithm relies on the fact that a windowed Fourier transform of the far field pattern of the wave radiated by a compactly supported source approximates an exponential ray transform with a purely imaginary exponent of a mollified version of the source. A filtered backprojection scheme for the standard ray transform applied to the absolute values of the windowed Fourier transform of the far field pattern is used to recover information on the support of the source. We provide the theoretical foundation of the method, discuss a numerical implementation of the fully three-dimensional algorithm, and present a series of numerical examples, including an inverse scattering problem, to s...