A multilevel fast multipole based approach for efficient reconstruction of perfectly conducting scatterers

A nonlinear reconstruction scheme based on the Distorted Born Iterative Method (DBIM) is presented to solve two-dimensional inverse scattering problems with metallic scatterers. Half-quadratic regularization alleviates the inherently ill-posed problem of nonlinear inverse scattering while simultaneously preserving edges. Reconstruction results are found by minimizing a cost function. A bistatic experimental set-up is studied with angular and frequency diversity. A Multilevel Fast Multipole Algorithm (MLFMA) combined with a conjugate gradient (CG) scheme is introduced to solve the forward as well as the inverse scattering problem involved in the DBIM. The computational complexity per CG iteration using the MLFMA is of order O(N log N) compared to O(N²) in a standard implementation without the MLFMA. Numerical reconstruction results obtained from synthetic scattering data are presented.