A problem of integral geometry for a family of curves with incomplete data

The unknown boundary problem of integral geometry is considered. Known data are integrals of unknown functions over an unknown family of curves in Euclidean space of any dimension. It is mentioned that, under the traditional approach, the integral geometry problem under consideration would be underdetermined. The sought object is the discontinuity surfaces of the integrands. A uniqueness theorem for the solution of the problem specified above is proved.