Inversion formulas for tensor imaging on incomplete data

In this article new inverse formulas for a ray transform of symmetric tensor fields with incomplete data are given. The Radon transform of Saint-Venant operator of tensor field is uniquely determined when the line integrals of the field along lines which form an $n$-dimensional complexes in the space $\mathbb{R}^n$ are given. Three most common complexes are considered: the family of lines intersecting a given curve, intersecting a given curve at infinity and tangent a given surface. In the case of the complex of lines intersecting a curve at infinite the formula, containing only two-fold integration is obtained.