A quantitative theory of scalar inverse scattering

A quantitative theory for 3-D inverse scattering is discussed. It is based on a formulation of the inverse problem in the whole space as a combination of the interior and exterior problems. The uniqueness of the solution, which is a major difficulty in most of the existing numerical approaches, can be managed through the eigenfunction expansion associated with the interior problem. The necessary data, another difficulty in the numerical approaches, can be acquired by a transformation of the measured data to the hologram, which is a function in the whole space. The corresponding integral equation results from a modification of the Porter-Borjarski equation. The merits of the approach are discussed.<>