We apply a Bayesian method for inferring an optimal basis to the problem
of finding efficient image codes for natural scenes. The bases learned
by the algorithm are oriented and localized in both space and spatial-frequency,
bearing a resemblance to two-dimensional Gabor functions, and increasing
the number of basis functions results in a greater sampling density in
position, orientation, and scale. These properties also resemble the spatial
receptive fields of neurons in the primary visual cortex of mammals, suggesting
that the receptive-field structure of these neurons can be accounted for
by a general efficient coding principle. The probabilistic framework provides
a method for comparing the coding efficiency of different bases objectively
by calculating their probability given the observed data or by measuring
the entropy of the basis function coefficients. The learned bases are shown
to have better coding efficiency than traditional Fourier and wavelet bases.
This framework also provides a Bayesian solution to the problems of image
denoising and filling-in of missing pixels. We demonstrate that the results
obtained by applying the learned bases to these problems are improved over
those obtained with traditional techniques.