An efficient optimization method for the reconstruction of multiple profiles

In this paper, we discuss the inverse problem of finding multiple profiles inside a scatterer using scattering data measured outside the scatterer, at fixed frequencies. We examine the case of TE mode electromagnetic scattering. In particular, we use a pure multipole expansions approach (instead of the combination of FEM and BEM) for solving the direct problem and an optimization method based on multipole approximations of the field for the inverse problem. This (realistic) approach for solving the inverse problem has obvious advantages, since it uses only elementary mathematics and much less time is needed for computing the Jacobian, etc.