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

Martin J. Wainwright, Eero P. Simoncelli, Alan S. Willsky

Research output: Contribution to journalArticlepeer-review


We develop a new class of non-Gaussian multiscale stochastic processes defined by random cascades on trees of multiresolution coefficients. These cascades reproduce a semiparametric 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.

Original languageEnglish (US)
Pages (from-to)89-123
Number of pages35
JournalApplied and Computational Harmonic Analysis
Issue number1
StatePublished - Jul 2001

ASJC Scopus subject areas

  • Applied Mathematics


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