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

M J Wainwright, E P Simoncelli, and A S Willsky

Published in Applied and Computational Harmonic Analysis, vol.11(1), pp. 89--123, Jul 2001.
DOI: 10.1117/12.408598

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    • We develop a new class of non-Gaussian multiscale stochastic processes defined by random cascades on trees of multiresolution coefficients. These cascades reproduce a semi-parametric class of random variables known as Gaussian scale mixtures, members of which include many of the best-known heavy-tailed distributions. This class of cascade models is rich enough to accurately capture the remarkably regular and non-Gaussian features of natural images, 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 image structure (e.g., edges). Our framework generates global yet structured image models, thereby providing a unified basis for a variety of applications in signal and image processing, including image denoising, coding and super-resolution.
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