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

M J Wainwright, E P Simoncelli, and A Willsky

Published in Proc SPIE, Conf. on Wavelet Applications in Signal and Image Processing VIII, vol.4119 pp. 229--240, Jul 2000.
© SPIE - the International Society for Optical Engineering, 2000

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    • 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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