An Inverse Fast Multipole Method for Geometry Reconstruction Using Scattered Field Information

A novel inverse fast multipole method (FMM) application for accelerating inverse problem solution is presented. The idea is based on the multipole expansion properties of the scattered fields and reconstructed equivalent currents, which allow an easy inversion of the FMM operators, resulting in a forward solution of the inverse problem, i.e., without matrix inversion or cost function minimization. In addition, this technique allows the use of reconstruction domain discretization larger than half a wavelength and overcomes the restriction of having the entire target enclosed by a reconstruction domain, features that also contribute to the reduction of calculation time. Two 3D application examples are presented, highlighting the achieved inverse FMM speed-up with respect to previous inverse scattering methods for geometry reconstruction.