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Proceedings Paper

Adapting overcomplete wavelet models to natural images
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Paper Abstract

Overcomplete wavelet representations have become increasingly popular for their ability to provide highly sparse and robust descriptions of natural signals. We describe a method for incorporating an overcomplete wavelet representation as part of a statistical model of images which includes a sparse prior distribution over the wavelet coefficients. The wavelet basis functions are parameterized by a small set of 2-D functions. These functions are adapted to maximize the average log-likelihood of the model for a large database of natural images. When adapted to natural images, these functions become selective to different spatial orientations, and they achieve a superior degree of sparsity on natural images as compared with traditional wavelet bases. The learned basis is similar to the Steerable Pyramid basis, and yields slightly higher SNR for the same number of active coefficients. Inference with the learned model is demonstrated for applications such as denoising, with results that compare favorably with other methods.

Paper Details

Date Published: 13 November 2003
PDF: 8 pages
Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); doi: 10.1117/12.508351
Show Author Affiliations
Phil Sallee, Univ. of California/Davis (United States)
Bruno A. Olshausen, Univ. of California/Davis (United States)

Published in SPIE Proceedings Vol. 5207:
Wavelets: Applications in Signal and Image Processing X
Michael A. Unser; Akram Aldroubi; Andrew F. Laine, Editor(s)

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