ABSTRACT
Inversion of the Radon transform was one of the first problems of integral geometry, which is a branch of mathematics dealing with the recovery of functions knowing their integrals over a family of manifolds. Radon’s paper was not used for a long time. The rapid development of applications of the Radon transform started in the early 1970s. Local tomography received an impulse in its development when the authors of this monograph discovered a family of local tomography functions, applied systematically methods of the theory of pseudodifferential operators to tomography, and introduced the new notions of pseudolocal and geometrical tomographies. The range of mathematical and numerical problems related to the Radon transform and computed tomography is extremely wide. X-ray transmission tomography is popular in medical diagnostics and in many industrial applications, where there is a need for nondestructive evaluation.
