A new data-based method for linear inverse scattering

In this contribution, we expand the repertoire of linearizing strategies pertinent to the inverse medium problem. This is accomplished by means of a new decomposition of the forward scattering map which reveals a previously unknown approximate forward scattering relation. The latter is data-driven, i.e., it involves exact scattering data, and leads to a new linear inverse scattering approach that generalizes and can be more broadly applicable than the classical Born approximation. The study is developed for a far-zone 2-D scalar case. Some simple numerical examples are added to check the theory.