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Proceedings Paper

Learning sparse overcomplete image representations
Author(s): Bruno A. Olshausen; K. Jarrod Millman
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Paper Abstract

We describe a method for learning an over complete set of basis functions for the purpose of modeling data with sparse structure. Such data re characterized by the fact that they require a relatively small number of non-zero coefficients on the basis functions to describe each data point. The sparsity of the basis function coefficients is modeled with a mixture-of-Gaussians distribution. One Gaussian captures non-active coefficients with a large-variance distribution centered at zero, while one or more other Gaussians capture active coefficients with a large-variance distribution. We show that when the prior is in such a form, there exist efficient methods for learning the basis functions as well as the parameters of the prior. The performance of the algorithm is demonstrated on a number of test cases and also on natural images. The basis functions learned on natural images are similar to those obtained with other methods, but the sparse from of the coefficient distribution is much better described. Also, since the parameters of the prior are adapted to the data, no assumption about sparse structure in the images need be made a priori, rather it is learned from the data.

Paper Details

Date Published: 4 December 2000
PDF: 8 pages
Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); doi: 10.1117/12.408632
Show Author Affiliations
Bruno A. Olshausen, Univ. of California/Davis (United States)
K. Jarrod Millman, Univ. of California/Davis (United States)

Published in SPIE Proceedings Vol. 4119:
Wavelet Applications in Signal and Image Processing VIII
Akram Aldroubi; Andrew F. Laine; Michael A. Unser, Editor(s)

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