Метод приближенного обращения для операторов преобразования Радона функций и нормального преобразования Радона векторных и симметричных $2$-тензорных полей в $\mathbb{R}^3$

We propose approach for reconstruction of a three-dimensional function from the known values of Radon transform. The approach is based on the method of approximate inverse. The obtained result is the basis of two approaches for reconstruction of a potential part of vector and symmetric $2$-tensor fields, which have form $\mathrm{d}\psi$, $\psi\in H^1_0(B)$ and $\mathrm{d}^2\psi$, $\psi\in H^2_0(B)$, respectively. Here $\mathrm{d}$ is the inner derivation operator, which is a composition of the operators of gradient and symmetrization. Initial data for the problems are the known values of normal Radon transform. The first approach allows to recover components of potential part of fields, and the second reconstructs a potential of potential part of fields.