Random Cascades on Wavelet Trees and Their Use in Analyzing and Modeling Natural Images

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

Research output: Contribution to journalArticle

Abstract

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
Volume11
Issue number1
DOIs
StatePublished - Jul 2001

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Cascade
Wavelets
Image denoising
Random processes
Modeling
Random variables
Scale Mixture
Signal processing
Image Model
Heavy-tailed Distribution
Image processing
Gaussian Mixture
Image Denoising
Super-resolution
Denoising
Multiresolution
Signal Processing
Stochastic Processes
Image Processing
Efficient Algorithms

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Random Cascades on Wavelet Trees and Their Use in Analyzing and Modeling Natural Images. / Wainwright, Martin J.; Simoncelli, Eero; Willsky, Alan S.

In: Applied and Computational Harmonic Analysis, Vol. 11, No. 1, 07.2001, p. 89-123.

Research output: Contribution to journalArticle

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