Sampling and Resolution

Abstract

In this chapter we want to find out how to properly sample Pf, Rf for some function f. We have seen in Theorem II.3.7 that f is basically undetermined by Pf (θ _j , x) for finitely many directions θ _j even in the semi-discrete case in which x runs over all of θ ¹_j . Therefore we have to restrict f somehow. It turns out that positive and practically useful results are obtained for (essentially) band-limited functions f. 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.