The approximate inverse in action with an application to computerized tomography

摘要

The approximate inverse is a scheme to obtain stable numerical inversion formulae for linear operator equations of the rst kind. Yet, in some applications the computation of a crucial ingredient, the reconstruction kernel, is time-consuming and instable. It may even happen that the kernel does not exist for a particular semidiscrete system. To cure this dilemma we propose and analyze a technique that is based on a singular value decomposition of the underlying operator. The results are applied to the reconstruction problem in 2D-computerized tomography where they enable the design of reconstruction filters and lead to a novel error analysis of the filtered backprojection algorithm. [References: 26]