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.