One-dimensional inverse scattering problems: an asymmetric two-component wave system framework

Abstract

Many one-dimensional inverse scattering problems can be formulated as a two-component wave system inverse problem, including inverse problems for lossless and absorbing acoustic and dielectric media. The advantage of doing so is that well known signal processing algorithms with good numerical stability properties can be used to reconstruct such media from either reflection or transmission responses to impulsive or harmonic sources. If the system is asymmetric, i.e. has different reflectivity functions in different directions, transmission data as well as reflection data are required. The author summarises algorithms for a wide variety of one-dimensional inverse problems, derives some new ones, and presents a simple framework that reveals much about these problems.