Inverse scattering

Abstract

We give a survey of the mathematical basis of inverse scattering theory, concentrating on the case of time-harmonic acoustic waves. After an introduction and historical remarks, we give an outline of the direct scattering problem. This is then followed by sections on uniqueness results in inverse scattering theory and iterative and decomposition methods to reconstruct the shape and material properties of the scattering object. We conclude by discussing qualitative methods in inverse scattering theory, in particular the linear sampling method and its use in obtaining lower bounds on the constitutive parameters of the scattering object.