On the fast multipole method applications for inverse problems

A novel inverse Fast Multipole Method (FMM) application for imaging applications is presented. The idea is based on the multipole expansion of the integral equations relating the scattered fields and equivalent currents. This kind of expansion allows 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. 3D application examples are presented, highlighting the achieved inverse FMM speed-up with respect to previous inverse source-based problem for geometry reconstruction.