Abstract: We prove uniqueness in inverse acoustic scattering in the case the density of the medium has an unbounded gradient across Σ⊂ΩΣ⊂Ω, where ΩΩ is a 3D-Lipschitz domain. The corresponding direct problem is related to the stationary waves scattering for 3D Schrödinger operators with δδ-type singular perturbations supported on ∂Ω∂Ω and of strength α∈Lp(∂Ω),p>2α∈Lp(∂Ω),p>2. This is a multiple scattering problem from obstacles and potentials whose solutions depend on the obstacles locations and shapes, the related transmission impedances and the background potentials. The inverse problem then consists in determining these scattering parameters from a complete set of far-field data at a fixed energy. In this framework, we show that the acoustic far-field pattern can be defined in terms of the scattering amplitude for the corresponding Schrödinger operator. A uniqueness result is then obtained by using new estimates for complex geometrical optics solutions (recently provided by B. Haberman for the Calderon's problem). This is a joint work with: M. Sini and A. Posilicano.