Random cascades on wavelet trees and their use in analyzing and modeling natural images

We develop a new class of non-Gaussian multiscale stochastic processes defi ned by random cascades on trees of multiresolution coefficients, These casc ades reproduce a semiparametric class of random variables known as Gaussian scale mixtures, members of which include many of the best known, heavy-tai led distributions. This class of cascade models is rich enough to accuratel y capture the remarkably regular and non-Gaussian features of natural image s, but also sufficiently structured to permit the development of efficient algorithms. In particular, we develop an efficient technique for estimation , and demonstrate in a denoising application that it preserves natural imag e structure (e.g,, edges). Our framework generates global yet structured im age models, thereby providing a unified basis for a variety of applications in signal and image processing, including image denoising, coding, acid su per-resolution. (C) 2001 Acadrmic Press