  Absorbing layers are sometimes required to be impractically thick in order to
offer an accurate approximation of an absorbing boundary condition for the
Helmholtz equation in a heterogeneous medium. It is always possible to reduce
an absorbing layer to an operator at the boundary by layer-stripping
elimination of the exterior unknowns, but the linear algebra involved is
costly. We propose to bypass the elimination procedure, and directly fit the
surface-to-surface operator in compressed form from a few exterior Helmholtz
solves with random Dirichlet data. The result is a concise description of the
absorbing boundary condition, with a complexity that grows slowly (often,
logarithmically) in the frequency parameter.
