The method of approximate inverse for the Radon transform operator acting on functions and for the normal Radon transform operators acting on vector and symmetric 2-tensor fields in R 3

摘要

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 elds, which have form dψ, ψ ∈ H1 0 (B) and d 2ψ, ψ ∈ H2 0 (B), respectively. Here 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 rst approach allows to recover components of potential part of elds, and the second reconstructs a potential of potential part of elds.