3. Sampling and Resolution
Frank Natterer · Society for Industrial and Applied Mathematics eBooks · 2001
In this chapter we want to find out how to properly sample Pƒ, Rƒ for some function ƒ. We have seen in Theorem II.3.7 that ƒ is basically undetermined by Pƒ(θj,x) for finitely many directions θj even in the semi-discrete case in which x runs over all of θj⊥ . Therefore we have to restrict ƒ somehow. It turns out that positive and practically useful results are obtained for (essentially) band-limited functions ƒ. These functions and their sampling properties are summarized in Section III.1. In Section III.2 we study the possible resolution if the Radon transform is available for finitely many directions. In Section III.3. we find the resolution of some fully discrete sampling schemes in the plane.