Stability of the inversion of 3D fixed-frequency scattering data

AbstractNumerical methods for solving 3D inverse scattering problems with fixed-energy data are described. Exact inversion formulas are given. Stability of the inversion methods based on these formulas is investigated. An explicit formula is given for construction of the Dirichlet-to-Neumann map from the scattering amplitude. This formula is used as a basis for another numerical approach to the inverse scattering problem. Several open problems are formulated