L. Paivarinta et al., RECONSTRUCTION OF SINGULARITIES OF A SCATTERING POTENTIAL IN 2 DIMENSIONS, Advances in applied mathematics, 15(1), 1994, pp. 97-113
In this paper, we consider the inverse scattering problem for the Schr
odinger equation in two dimensions. This problem of reconstructing the
scattering potential from the far field data has a well-known approxi
mate solution based on the linearization through the weak scatterer (o
r Born) approximation. In the present work it is shown that while this
approximate solution need not be close to the underlying scattering p
otential, the leading local singularities of the potential are recover
ed exactly in this procedure. (C) 1994 Academic Press, Inc.