Reconstruction of Singularities of a Scattering Potential in Two Dimensions

AbstractIn this paper, we consider the inverse scattering problem for the Schrödinger equation in two dimensions. This problem of reconstructing the scattering potential from the far field data has a well-known approximate solution based on the linearization through the weak scatterer (or Born) approximation. In the present work it is shown that while this approximate solution need not be close to the underlying scattering potential, the leading local singularities of the potential are recovered exactly in this procedure