Linearised inverse scattering in attenuating media

A theoretical basis for inverse scattering from three-dimensional objects embedded in a dispersive attenuating background is presented within the first Born approximation. It is shown that suitable processing of the time-dependent scattered field data generated by an incident wave pulse allows the inverse problem for attenuating backgrounds to be mapped into the corresponding problem for non-attenuating backgrounds, for which a number of reconstruction algorithms have been developed. The paper includes a detailed discussion of the inversion procedure for electromagnetic inverse scattering from localised perturbations in the complex index of refraction of a conduction medium.