On the Uniqueness of the Solution of the Inverse Coefficient Problem for the Helmholtz Equation in a Phaseless Spatially Nonoverdetermined Statement

Abstract We establish the uniqueness of the solution of the inverse problem for the Helmholtz equation in which the refraction coefficient, which describes the properties of a bounded inhomogeneity in a wave medium, is sought. The initial data for determining the desired coefficient are the absolute values of the solutions corresponding to either point sources concentrated on a segment or spherically symmetric distributed sources with centers on the segment. The measurements of the wave field are carried out in a plane domain that does not meet the inhomogeneity localization area.