Adapting overcomplete wavelet models to natural images

Phil Sallee; Bruno A. Olshausen

doi:10.1117/12.508351

13 November 2003 Adapting overcomplete wavelet models to natural images

Phil Sallee, Bruno A. Olshausen

Proceedings Volume 5207, Wavelets: Applications in Signal and Image Processing X; (2003) https://doi.org/10.1117/12.508351
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

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.

Citation Download Citation

Phil Sallee and Bruno A. Olshausen "Adapting overcomplete wavelet models to natural images", Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); https://doi.org/10.1117/12.508351

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KEYWORDS

Wavelets

Denoising

Signal to noise ratio

Image filtering

Spatial frequencies

Databases

Image compression

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