The method of approximate inverse for the normal Radon transform operator

Abstract

Abstract We propose an approach for reconstructing a three-dimensional function from the known values of the Radon transform. The approach is based on the method of approximate inverse. The result obtained is the basis of two approaches for reconstructing a potential part of the vector and symmetric 2-tensor fields from the known values of the normal Radon transform. The first approach allows the recovery of components of the potential part of fields, and the second one reconstructs a potential of the potential part of fields.