Reconstruction for novel sampling structures

We examine the problem of reconstructing a signal from periodic non-uniform samples, i.e. a uniform train from which samples are deleted in some periodic fashion. We develop a condition previously derived by Herley and Wong (see Proc. IEEE Int. Conf. Image Proc., 1996) and examine its implications. We show that this method has a number of advantages over alternative approaches. In particular it gives a condition for achieving the minimum rate rather than approaching it asymptotically. We show that it generally leads to a reconstruction scheme that is simpler than those derived by other strategies. We examine a few special cases in which the minimum rate is precisely achieveable, and cases where design of the reconstruction system is possible without explicitly knowing the signal spectrum