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 wavelet or other multiresolution coefficients. These cascades reproduce a rich semi-parametric class of random variables known as Gaussian scale mixtures. We demonstrate that this model class can accurately capture the remarkably regular and non-Gaussian features of natural images in a parsimonious fashion, involving only a small set of parameters. In addition, this model structure leads to efficient algorithms for image processing. In particular, we develop a Newton-like algorithm for MAP estimation that exploits very fast algorithms for linear-Gaussian estimation on trees, and hence is efficient. On the basis of this MAP estimator, we develop and illustrate a denoising technique that is based on a global prior model, and preserves the structure of natural images (e.g., edges).

Original languageEnglish (US)
Pages (from-to)229-240
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - Feb 4 2000


  • Denoising
  • Natural images
  • Random cascades
  • Statistical models
  • Wavelets

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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