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

Martin Wainwright, Eero P Simoncelli, and Alan Willsky

Appears in:
Applied and Computational Harmonic Analysis
Volume 11, Number 1, pp 89-123, July 2001.
Special issue on wavelet applications.

We develop a new class of non-Gaussian multiscale stochastic processes de ned by random cascades on trees of multiresolution coe cients. 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 su ciently structured to permit the development of e cient algorithms. In particular, we develop an e cient 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 uni ed basis for a variety of applications in signal and image processing, including image denoising, coding and super-resolution.
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