Analytical and numerical reconstruction of internal structure of the objects in a family of straight-line segments

We considered a problem of reconstruction function in a strip, if we know the integrals of sought function in the family of straight-line segments with a given weight function of a special kind. We obtained an analytical representation of solution in the class of smooth finite functions, the uniqueness theorems for solution of the problem is proved. The stability estimate of solution in Sobolev spaces is presented, which implies its weakly ill-posedness. These theoretical results are used in order to recover the internal structure objects from their integral data. Numerical results and their graphical representation are given.