Underdetermination in an Integral Geometry Problem

A uniqueness theorem is presented for the problem of determining an unknown boundary under general constraints and under a condition that guarantees the existence of the desired surfaces. An n-dimensional arithmetic space and a sum of integrals of unknown functions along unknown straight lines is considered. Two systems of subdomains of the certain operators and the functions that satisfy some conditions formulated are also considered. For any function from a certain class, the function has continuous first partial derivatives that are bounded on any non-empty set. if the surface is determined from anomalously large values of weight functions that can serve as a filter.