Random Cascades on Wavelet Trees and Their Use in Analyzing and Modeling Natural Images
✍ Scribed by Martin J. Wainwright; Eero P. Simoncelli; Alan S. Willsky
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 804 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1063-5203
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✦ Synopsis
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.