  We study the inverse scattering for Schr{\"o}dinger operators on locally
perturbed periodic lattices. We show that the associated scattering matrix is
equivalent to the Dirichlet-to-Neumann map for a boundary value problem on a
finite part of the graph, and reconstruct scalar potentials as well as the
graph structure from the knowledge of the S-matrix. In particular, we give a
procedure for probing defects in hexagonal lattices (graphene).
