Quantitative Non-Linear Inverse Scattering: A Wealth of Possibilities Through Smart Rewritings of the Basic Equations

Non-linearity arising from mutual interactions is one of the two main difficulties to be addressed in inverse scattering. In this paper, we first review and describe under a common rationale some approaches which have been introduced in literature in order to counteract non-linearity. In particular, we focus on possible rewritings of the Lippman Schwinger basic equation such to reduce the `degree of non-linearity' of inverse scattering problem. In detail, three different rewritings are discussed and compared by emphasizing similarities and differences, and in the same `rewriting' spirit, we also summarize and discuss the `Virtual Experiments' framework. Then, some possible and effective joint exploitations of the above concepts are introduced, discussed and tested against numerical examples.