Quasi-Born approximation prefiltering for noniterative inverse scattering

We study and illustrate quasi-Born approximation conditions which allow the solution of certain inverse scattering problems without iterations even though the corresponding forward map from scatterer to data is in general nonlinear due to multiple scattering. The proposed methodology focuses on a form of linearizing prefiltering which sheds fundamental, quantitative insight on the possibilities and challenges associated to solving certain inverse scattering problems without iterations.