Uncertainty Principles for Three-Dimensional Inverse Source Problems
Uncertainty Principles for Three-Dimensional Inverse Source Problems
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DOI：
10.1137/17m111287x
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发表时间：
2017-11
期刊：
影响因子：
--
通讯作者：
Roland Griesmaier;J. Sylvester
中科院分区：
文献类型：
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作者：
Roland Griesmaier;J. Sylvester
最近在[R.Griesmaier和J.Sylvester，SIAM J.Appl]中建立了新的测不准原理，适用于二维自由空间中由分离良好的局域源集合辐射的时间谐声波或电磁波的远场。数学，77(2017)，第154--180页]。这些不确定原理已被用来开发稳定性估计和重建算法，用于恢复每个单独源辐射的远场，并同时恢复丢失的数据段。在这篇文章中，我们给出了这些不确定原理在相关的三维环境中的推广。我们考虑了用于远场分裂和数据完成的重建方案的扩展，包括它们的稳定性分析，并讨论了我们的结果在三维情况下的锐性。我们简要地评论了重建算法的数值实现，并给出了一个数值例子。
Novel uncertainty principles for far fields of time-harmonic acoustic or electromagnetic waves radiated by collections of well-separated localized sources in two-dimensional free space have recently been established in [R. Griesmaier and J. Sylvester, SIAM J. Appl. Math., 77 (2017), pp. 154--180]. These uncertainty principles have been utilized to develop stability estimates and reconstruction algorithms for the recovery of the far field radiated by each of the individual sources, and the simultaneous restoration of missing data segments. In this paper, we present generalizations of these uncertainty principles for a relevant three-dimensional setting. We consider extensions of the reconstruction schemes for far field splitting and data completion, including their stability analysis, and we discuss the sharpness of our results in the three-dimensional case. We briefly comment on the numerical implementation of the reconstruction algorithms and include a numerical example.