Tomography of tensor fields in the plane

The problems of tomography and integral geometry of tensor fields in the plane are considered. Basic backgrounds on tensor fields, operators of ray transforms and back-projections are stated. The representations of symmetric tensor fields through potential that generates the field with usage of operators of differentiation and symmetrization are obtained. A detailed classification of symmetric m-tensor fields is suggested and decomposition theorems are obtained. Back-projection operators acting on ray transforms of tensor fields are introduced. The kernels and images of the operators of mixed and transverse ray transforms are described. The connections between ray transforms of the fields and Radon transforms of their potentials are established. The inversion formulas for the components of a field and for its potential are obtained.