Kernel-based deterministic blue-noise sampling of arbitrary probability density functions

Abstract

This paper provides an efficient method for approximating a given continuous probability density function (pdf) by a Dirac mixture density. Optimal parameters are determined by systematically minimizing a distance measure. As standard distance measures are typically not well defined for discrete densities on continuous domains, we focus on shifting the mass distribution of the approximating density as close to the true density as possible. Instead of globally comparing the masses as in a previous paper, the key idea is to characterize individual Dirac components by kernel functions representing the spread of probability mass that is appropriate at a given location. A distance measure is then obtained by comparing the deviation between the true density and the induced kernel density. This new method for Dirac mixture approximation provides high-quality approximation results, can handle arbitrary pdfs, allows considering constraints for, e.g., maintaining certain moments, and is fast enough for online processing.