Using fundamental solutions in inverse scattering

We provide a brief description of recent results in inverse scattering theory having as a common mathematical framework the exploitation of the behaviour of the fundamental solution to the Helmholtz equation, in particular the fact that for the source point on the boundary partial derivative D of the scattering object such a solution is not in the Sobolev space H-1/2(partial derivative D). Included in our discussion are uniqueness theorems, decomposition methods (including the point-source method), the method of singular sources, the linear sampling method and the factorization method.