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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