Minimal Non-Uniform Sampling For Multi-Dimensional Period Identification

This paper addresses a fundamental question in the context of multi-dimensional periodicity. Namely, to distinguish between two N-dimensional periodic patterns, what is the least number of (possibly non-contiguous) samples that need to be observed? This question was only recently addressed for one-dimensional signals. This paper generalizes those results to N-dimensional signals. It will be shown that the optimal sampling pattern takes the form of sparse and uniformly separated bunches. Apart from new theoretical insights, this paper’s results may provide the foundation for fast N-dimensional period recognition algorithms that use minimal number of samples1.