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Abstract:
We examine the statistics of natural monochromatic images
decomposed using a multi-scale wavelet basis. Although the
coefficients of this representation are nearly decorrelated, they
exhibit important higher-order statistical dependencies that cannot
be eliminated with purely linear processing. In particular,
rectified coefficients corresponding to basis functions at
neighboring spatial positions, orientations and scales are highly
correlated. A method of removing these dependencies is to divide
each coefficient by a weighted combination of its rectified
neighbors. Several successful models of neural processing in visual
cortex are based on such divisive gain control
(or``normalization'') computations, and thus our analysis provides
a theoretical justification for these models. Perhaps more
importantly, the statistical measurements explicitly specify the
weights that should be used in computing the normalization signal.
We demonstrate that this weighting is qualitatively consistent with
recent physiological measurements, and thus that early visual
neural processing is well matched to these statistical properties
of images
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