# Inversion formulas for tensor imaging on incomplete data

### DOI: 10.31029/demr.2.6

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 complex 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.

Keywords: symmetric tensor field, ray transform, reconstruction formula, complex of lines, Radon transform, solenoidal part, Saint-Venant operator.

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