Olshausen BA, Sallee P, Lewicki MS  (2001).  Learning Sparse Image Codes using a Wavelet Pyramid Architecture.  Advances in Neural Information Processing Systems, 12: 887-893.

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 of a linear superposition of sparse, independent components.  When adapted to natural images, the wavelet bases take on different orientations and they evenly tile the orientation domain, in stark contrast to the standard, non-oriented wavelet bases used in image compression.  When the basis set is allowed to be overcomplete, it also yields higher coding efficiency than standard wavelet bases.