Multiresolution Stochastic Models and Their Use in Modeling and Analysis of Random Processes and Fields
Monday, October 16, 2000 - 11:00am - 12:00pm
Alan Willsky (Massachusetts Institute of Technology)
In this talk we describe a body of research concerned with the building and exploitation of multiresolution statistical models of random phenomena and imagery. We begin with a discussion of linear stochastic models on multiresolution trees, in particular discussing the very efficient algorithms these models admit, the realization of random phenomena using such models, some relationships to wavelet decompositions of signals and images, and applications of this formalism, and some of its critical limitations. Motivated by two of these limitations, we describe two research directions that use this basic formalism as a point of departure. The first of these is a class of nonlinear models we refer to as wavelet cascades, which maintain much of the exploitable structure of our linear-tree models but allow us to capture distinctive nonlinear characteristics of natural imagery. The second is the examination of stochastic models on graphical structures other than trees, a topic of considerable interest in a number of quite different domains.