Weighted Radon Transforms of Three-Dimensional SymmetricTensor Fields of Rank Two

We study properties of weighted Radon transforms of symmetric $$ 2 $$ -tensor fields in R³ . We establish connections between weighted Radon transforms of $$ 2 $$ -tensor fields and the Radon transform of their potentials. These connections describe the kernel and image of tomographic integral operators acting on tensor fields. We consider formulations of problems on reconstruction of symmetric $$ 2 $$ -tensor fields from the values of the normal, longitudinal, and weighted Radon transforms and obtain inversion formulas.