  We consider a restricted Dirichlet-to-Neumann map associated to a wave type
operator on a Riemannian manifold with boundary. The restriction corresponds to
the case where the Dirichlet traces are supported on one subset of the boundary
and the Neumann traces are restricted on another subset. We show that the
restricted Dirichlet-to-Neumann map determines the lower order terms in the
wave equation, up the natural gauge invariances, along a convex foliation of
the manifold. We allow the lower order terms to be non-self-adjoint, and in
particular, the corresponding physical system may have dissipation of energy.
