A General Theory Of Time-sequential Sampling
Mohammad Rahgozar, Jan P. Allebach · 2005
In this paper, we consider the problem of optimum sampling of spatiotemporal signals. Recently, there has been increasing interest in this topic partly due to the advent of next generation television systems, and partly due to the growing need for sophisticated real time vision modules used in a variety of motion estimation and tracking tasks. Time-sequential sampling is a sampling paradigm in which samples are taken from the signal, one at a time, according to a prescribed ordering which is repeated after one complete frame of data is acquired. This paper extends previous work on time-sequential sampling [l] to include sampling on lattices with arbitrary geometries as well as sampling patterns which are replicated with arbitrary periodicities on these lattices. As a result, a unifying theory is developed which includes such classical field-instantaneous patterns as field-quincunx (body-centered orthorhombic lattice) and line-quincunx (hexagonal lattice with four field periodicity), proposed for downsampling of high-definition television signals, as specific examples. In this context, downsampling, e.g. from 2:l line-interlaced to one of the above patterns, can be analyzed in a straightforward manner. Such a treatment of downsampling also provides a systematic way for studying the aliasing effects of the ordering in which a signal is downsampled. The design and analysis of time-sequential sampling patterns is facilitated by introducing a powerful technique from the geometry of numbers which permits these tasks to be carried out in a coordinate system where the time-sequential patterns are rectangularly periodic. The resulting anti-aliasing patterns have a congruential structure. By further extending the theory to include time-sequential sampling on selected cosets of a lattice, we can analyze those sampling strategies for which the spectral replications are not confined to a geometrical lattice. This is the case with the bit-reversed sampling pattern.