Smart Rewritings of the Basic Equations for Quantitative Non-Linear Inverse Scattering

TL;DR

This paper reviews and compares methods for rewriting the fundamental equations in nonlinear inverse scattering to reduce nonlinearity, including numerical testing of combined approaches within a Virtual Experiments framework.

Contribution

It introduces and analyzes three novel rewriting strategies of the Lippman Schwinger equation to mitigate nonlinearity in inverse scattering problems.

Findings

Rewritings reduce the nonlinearity degree in inverse scattering equations.

Comparative analysis highlights similarities and differences among the approaches.

Numerical experiments demonstrate the effectiveness of combined strategies.

Abstract

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