Eero Simoncelli, Odelia Schwartz
We examine the statistics of natural monochromatic images decomposed using a multi-scale wavelet basis. Although the coefficients of this rep(cid:173) resentation are nearly decorrelated, they exhibit important higher-order statistical dependencies that cannot be eliminated with purely linear pro(cid:173) c~ssing. In particular, rectified coefficients corresponding to basis func(cid:173) tions 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. Sev(cid:173) eral successful models of the steady -state behavior of neurons in primary visual cortex are based on such "divisive 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 re(cid:173) cent physiological experiments that characterize the suppressive effect of stimuli presented outside of the classical receptive field. Our obser(cid:173) vations thus provide evidence for the hypothesis that early visual neural processing is well matched to these statistical properties of images.