Solution of the vectorial 3D inverse source problem by adjoint near-field fast multipole translations

A fast imaging algorithm based on adjoint near-field fast multipole translations and hierarchical multilevel disaggregations is presented to solve the full vectorial 3D inverse source problem. The problem formulation is related to the plane wave based near-field far-field transformation, where the inverse problem is solved iteratively. Our algorithm, however, only requires a single processing step. The described algorithm produces very good results in numerical tests with observation data of full spherical coverage.