We apply a Bayesian method for inferring an optimal basis to the
problem of finding efficient image codes for natural scenes. The
basis functions learned by the algorithm are oriented and localized in
both space and frequency, bearing a resemblance to 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 compared to
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.
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