Universal bounds for the sampling of graph signals

Sampling is a fundamental topic in graph signal processing with applications in estimation, clustering, and video compression. In contrast to traditional signal processing, however, the irregularity of the signal domain makes the selection of the sampling points non-trivial and hard to analyze. Indeed, although graph signal reconstruction is well-understood in the noiseless case, performance bounds for the interpolation of noisy samples exist mainly for randomized sampling schemes. This paper addresses this issue by deriving a lower bound on the mean-square interpolation error for graph signals. This bound is universal in the sense that it is not restricted to a specific sampling method and holds for all sampling sets. Simulations illustrate the tightness of the bound, which is then used to evaluate the performance of greedy sampling. Finally, a solution to the complexity issues of kernel principal component analysis is proposed using graph signal sampling.