Abstract:
The paper considers the vector tomography problem of reconstructing a three-dimensional vector field based on the values of unweighted (normal and longitudinal) and weighted Radon transforms. Using the detailed decomposition of vector fields obtained in the paper, connections are established between the unweighted and weighted Radon transforms acting on vector fields and the Radon transform acting on functions. In particular, the kernels of tomographic integral operators acting on vector fields are described. Some statements of tomography problems for the reconstruction of vector fields are considered, and inversion formulas for their solution are obtained.
Keywords:vector tomography, decomposition of vector field, normal Radon transform, longitudinal Radon transform, weighted Radon transform, inversion formula.
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