Learning sparse overcomplete image representations

Bruno A. Olshausen; K. Jarrod Millman

doi:10.1117/12.408632

4 December 2000 Learning sparse overcomplete image representations

Bruno A. Olshausen, K. Jarrod Millman

Proceedings Volume 4119, Wavelet Applications in Signal and Image Processing VIII; (2000) https://doi.org/10.1117/12.408632
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

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.

Citation Download Citation

Bruno A. Olshausen and K. Jarrod Millman "Learning sparse overcomplete image representations", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); https://doi.org/10.1117/12.408632

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