A two-dimensional medium is considered in which the fields are described by the Helmholtz equation. The linearized formulation of the problem of restoring the parameters of the medium (the inverse problem for the Helmholtz equation) is studied. The conditions for the uniqueness of detection of thin conducting layers are established. Examples are given of the multivaluedness of the solution of the inverse problem in information, which was initially thought to be even redundant for an unambiguous solution.