Learning sparse wavelet codes for natural images
Bruno A. Olshausen, Phil A. Sallee, Michael S. Lewicki · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2000
We show how a wavelet basis may be adapted to best represent natural images in terms of sparse coefficients. The wavelet basis, which may be either complete or overcomplete, is specified by a small number of spatial functions which are repeated across space and combined in a recursive fashion so as to be self-similar across scale. These functions are adapted to minimize the estimated code length under a model that assumes images are composed as a linear superposition of sparse, independent components. When adapted to natural images, the wavelet bases become selective to different spatial orientations, and they achieve a superior degree of sparsity on natural images as compared with traditional wavelet bases.