Near-Field and Far-Field Imaging by Hierarchical Wave Field Representations in k-Space

传播平面波的分层波场表示已被证明是非常有用的，当需要评估大量观测位置中的分布式电磁源的波场时。在积分方程的数值解中，这些基本概念被用来创建所谓的快速多极和多层快速多极方法，它们彻底改变了积分方程的数值解，被认为是过去世纪的十大数值算法。近年来，分层波场表示的范围已扩展到近场/远场变换和反演震源问题，并取得了巨大的成功。在这个项目中，我们建议解决单基地和双基地成像问题，在远场和近场条件下，任意成像天线的位置和任意成像天线的特性，利用分层波场表示与传播平面波。将以适当的形式建立主动成像配置的双向波传播算子，用于分层表示和在近场和远场条件下利用快速多极平移算子。各种成像算法将制定，实施和研究基于这些概念。预期可以实现成像算法，其与可用方法相比提供显著改进的灵活性、效率和准确性。新的成像方法将通过综合生成的数据和测量进行验证。如有可能，还将把新算法与已确立的成像概念或其他研究小组的成像概念进行比较，以定期采样数据或降低复杂性的数据，以便能够评估各种方法的性能，并提出使用建议。该项目将基于计算电磁学概念到基于测量数据的成像领域的后续转移。然而，我们也希望通过成像的经验为我们的计算电磁学研究提供新的见解。

Hierarchical wave field representations with propagating plane waves have been proven extremely useful, whenever the wave fields of distributed electromagnetic sources in a large collection of observation locations need to be evaluated. In the numerical solution of integral equations, these basic concepts have been utilized in order to create the so-called fast multipole and multilevel fast multipole methods, which revolutionized numerical integral equation solutions and which are considered as top ten numerical algorithms of the past century. Recently, the scope of hierarchical wave field representations has been extended to near-field/far-field transformations and inverse source problems with great success. In this project, we propose to solve monostatic and bistatic imaging problems under far-field and near-field conditions, with arbitrary imaging antenna locations and with arbitrary imaging antenna characteristics by utilizing hierarchical wave field representations with propagating plane waves. The two-way wave propagation operators of the active imaging configuration will be set up in appropriate form for the hierarchical representation and for the utilization of the fast multipole translation operators under near-field and far-field conditions. Various imaging algorithms will be formulated, implemented and investigated based on these concepts. It is expected that imaging algorithms can be realized, which provide for considerably improved flexibility, efficiency and accuracy as compared to available methods. The new imaging methods will be validated by synthetically generated data and by measurements. If possible, the new algorithms will also be compared to established imaging concepts or with imaging concepts of other research groups for regularly sampled data or for data with reduced complexity in order to be able to evaluate the performance of the various approaches and give recommendations for their use. The project will be based on a consequent transfer of computational electromagnetics concepts into the field of measurement data based imaging. However, we do also expect to gain new insights for our computational electromagnetics research by the experiences with imaging.