Reconstruction of a potential from the impedance boundary map

We consider the inverse boundary value problem for the Schrodinger equation at xed energy with boundary measurements represented as the impedance boundary map (or Robin-to-Robin map). We give formulas and equations for nding (generalized) scattering data for the aforementioned equation from boundary measurements in this impedance representation. Combining these results with results of the inverse scattering theory we obtain ecient methods for reconstructing potential from the impedance boundary map. To our knowledge, results of the present work are new already for the case of Neumann-to-Dirichlet map.