An Inverse Fast Multipole Method for Imaging Applications

An inverse fast multipole method (FMM) for imaging applications is presented. The goal is the acceleration of an inverse source-based method for geometry reconstruction achieved by taking advantage of the multipole expansion properties of the scattered fields and reconstructed equivalent currents. By conjugating the FMM terms, it is possible to recover the equivalent currents from the scattered fields in just one step rather than using matrix inversion or cost function minimization. For the sake of simplicity, 2-D problems where the objects under test having symmetry along one dimension are considered.