Multiscale representations of Markov random fields

A framework for multiscale stochastic modeling was introduced (K.C. Chou et al., 1989) based on coarse-to-fine scale-recursive dynamics defined on trees. This model class has some attractive characteristics which lead to extremely efficient, statistically optimal signal and image processing algorithms. In the present work, the authors describe how 1-D Markov processes and 2-D Markov random fields (MRFs) can be represented within this framework. In addition, they propose a framework for reduced-order multiscale modeling of Gaussian MRFs.<>