Iryna Egorova and Gerald Teschl Reconstruction of the Transmission Coefficient for Steplike Finite-Gap Backgrounds (28K, LaTeX2e) ABSTRACT. We consider scattering theory for one-dimensional Jacobi operators with respect to steplike quasi-periodic finite-gap backgrounds and show how the transmission coefficient can be reconstructed from minimal scattering data. This generalizes the Poisson-Jensen formula for the classical constant background case.