An underdetermined problem of integral geometry for the generalized radon transform

Abstract

Under study is a new problem of integral geometry. All kinds of planes are considered in the three-dimensional Euclidean space. The available data are given by the integrals over all these planes of an unknown piecewise-smooth function depending both on the spatial variables and the variables characterizing the planes. The sought object is a first kind discontinuity surface of the integrand. The uniqueness theorem of a desired surface is proved. The above results are related to one of the aspects of the theory of testing unknown media by various physical signals.