NONUNIFORM SAMPLING AND RECONSTRUCTION

Publisher Summary This chapter discusses the signal processing theory behind nonuniform sampling. Nonuniform signal processing has become important in computer graphics in recent years for two principal reasons; it offers the chance to use variable sampling density, and it allows trading structured aliasing for noise. All of the signal processing theory has been built on the assumption that samples are regularly spaced by an equal amount. Many rough samples might combine to give an equally useful representation of the signal as a smaller number of accurate samples, at less cost, although interval analysis has appeared in computer graphics. Another alternative is to move the samples off the regular, uniform pattern. Stochastic sampling is thus a special form of nonuniform sampling where the samples are aperiodic, meaning that there is no single structure that is repeated by translation at equal intervals across the domain. As there is no repeated unit, there is no pattern associated with aperiodic sampling, but rather just a single arrangement of samples.