Uncertainty principles for inverse source problems for electromagnetic and elastic waves
Uncertainty principles for inverse source problems for electromagnetic and elastic waves
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DOI：
10.1088/1361-6420/aab45c
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发表时间：
2018-06
期刊：
影响因子：
2.1
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
在各向同性均匀介质中，由压缩支撑的体电流辐射的时谐电磁波的远场和由压缩支撑的体力密度辐射的弹性波可以以非常相似的方式建模。两者都是向量值源项的投影限制傅立叶变换。在这项工作中，我们将Griesmaier和西尔维斯特（2017 SIAM J. Appl. Math. 77 154-80）最近为标量值时谐波的远场开发的两种类型的不确定性原理推广到这个向量值设置。这些不确定性原则产生的稳定性标准和算法分裂成远场辐射的远场辐射的个别源组件的集合分离的源，并恢复丢失的数据段。我们讨论适当的正则化策略，这些反问题，提供新的不确定性原则的基础上的稳定性估计，并评论重建计划。一个数值例子说明了我们的理论研究结果。
In isotropic homogeneous media, far fields of time-harmonic electromagnetic waves radiated by compactly supported volume currents, and elastic waves radiated by compactly supported body force densities can be modelled in very similar fashions. Both are projected restricted Fourier transforms of vector-valued source terms. In this work we generalize two types of uncertainty principles recently developed for far fields of scalar-valued time-harmonic waves in Griesmaier and Sylvester (2017 SIAM J. Appl. Math. 77 154–80) to this vector-valued setting. These uncertainty principles yield stability criteria and algorithms for splitting far fields radiated by collections of well-separated sources into the far fields radiated by individual source components, and for the restoration of missing data segments. We discuss proper regularization strategies for these inverse problems, provide stability estimates based on the new uncertainty principles, and comment on reconstruction schemes. A numerical example illustrates our theoretical findings.