Solution to the Full Vectorial 3-D Inverse Source Problem by Multilevel Fast Multipole Method Inspired Hierarchical Disaggregation

Abstract

A 3-D imaging approach based on a multilevel fast multipole method inspired hierarchical disaggregation of the broadband plane wave spectrum is introduced to solve the full vectorial electromagnetic inverse source problem based on the knowledge of the radiated fields. In terms of complexity, this algorithm is identical to fast Fourier transform accelerated 3-D imaging techniques. In terms of applicability, the hierarchical disaggregation is advantageous for commonly encountered spherical <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$k$</tex> </formula> -space data. Since the method can be directly combined with the near-field fast multipole translations, both far- and near-field data can be handled conveniently. The investigation includes an analysis of the inherent point spread function and numerical results.