ABSTRACT
Local tomography is attractive because it does not require collecting and processing of the tomographic data of the whole object if one is interested only in finding discontinuities inside a certain part of the object — the reconstruction at a point requires the knowledge of integrals of the density function along lines close to that point. This chapter introduces the alternative concept: pseudolocal tomography. The pseudolocal tomography function, on one hand, has locality properties and, on the other hand, preserves sizes of discontinuities of the original density function and of its derivatives. Moreover, images of discontinuities computed from the pseudolocal tomography function are also sharper than those in standard (global) tomography. The chapter discusses numerical implementation of pseudolocal tomography and presents results of its testing on synthetic tomographic data. It develops the generalization of pseudolocal tomography to the exponential Radon transform.
