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

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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.