The reconstruction of discrete sets from their projections is a frequently studied field in discrete tomography with applications in electron microscopy, image processing, radiology, and so on. Several efficient reconstruction algorithms have been developed for certain classes of discrete sets having some good geometrical properties. On the other hand, it has been shown that the reconstruction under certain circumstances can be very time-consuming, even NP-hard. In this chapter we show how prior information that the set to be reconstructed consists of several components can be exploited in order to facilitate the reconstruction. We present some general techniques to decompose a discrete set into components knowing only its projections and thus reduce the reconstruction of a general discrete set to the reconstruction of single components, which is usually a simpler task.

%B ADVANCES IN DISCRETE TOMOGRAPHY AND ITS APPLICATIONS %S Applied and Numerical Harmonic Analysis %I Birkhauser Boston %C Cambridge %P 153 - 173 %8 2007 %@ 978-0-8176-3614-2 %G eng %9 Book chapter %R 10.1007/978-0-8176-4543-4_8