Random Cascades on Wavelet Trees and Their Use in
Modeling and Analyzing Natural Imagery
Published in:
Proc 45th Annual Meeting of SPIE
San Diego, CA. July 2000.
© SPIE - the International Society for Optical Engineering, 2000.
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).
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