Random cascades on wavelet trees and their use in analyzing and modeling natural images

Martin J. Wainwright; Eero P. Simoncelli; Alan S. Willsky

doi:10.1117/12.408598

4 December 2000 Random cascades on wavelet trees and their use in analyzing and modeling natural images

Martin J. Wainwright, Eero P. Simoncelli, Alan S. Willsky

Proceedings Volume 4119, Wavelet Applications in Signal and Image Processing VIII; (2000) https://doi.org/10.1117/12.408598
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

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 algorithm 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.

Citation Download Citation

Martin J. Wainwright, Eero P. Simoncelli, and Alan S. Willsky "Random cascades on wavelet trees and their use in analyzing and modeling natural images", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); https://doi.org/10.1117/12.408598

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