The approximate inverse in action with an application to computerized tomography

The approximate inverse is a scheme to obtain stable numerical inversion fo rmulae for linear operator equations of the rst kind. Yet, in some applicat ions the computation of a crucial ingredient, the reconstruction kernel, is time-consuming and instable. It may even happen that the kernel does not e xist 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 prob lem in 2D-computerized tomography where they enable the design of reconstru ction filters and lead to a novel error analysis of the filtered backprojec tion algorithm.