A hybrid method for inverse scattering for shape and impedance

We present a hybrid method to numerically solve the inverse scattering problem for shape and impedance, given the far-field pattern for one incident direction. This method combines ideas of both iterative and decomposition methods, inheriting the advantages of each of them, such as getting good reconstructions and not needing a forward solver at each step. An optimization problem is presented as the theoretical background of the method and numerical results show its feasibility.