Stochastic pyramids for multiscale signal synthesis and analysis

Multiscale techniques require that signals are fitted to pyramid structures, with each level of the pyramid corresponding to a reduced-resolution approximation of the signal. Unlike deterministic pyramids, stochastic pyramids can be applied to signals characterized by some form of uncertainty. A number of fundamental properties of stochastic pyramids are studied, and advantages and disadvantages of various pyramid structures are discussed. Furthermore, the stochastic pyramid transform is proposed, as a solution to all problems associated with traditional stochastic pyramids. We briefly argue that this transform naturally leads to the multigrid Monte Carlo method, proposed by Goodman and Sokal (1989), which is mainly used to generate Markov random field images