Nonlinear and extra-classical receptive field properties and the statistics of natural scenes

The neural mechanisms of early vision can be explained in terms of an infor mation-theoretic optimization of the neural processing with respect to the statistical properties of the natural environment. Recent applications of t his approach have been successful in the prediction of the linear filtering properties of ganglion cells and simple cells, but the relations between t he environmental statistics and cortical nonlinearities, like those of end- stopped or complex cells, are not yet fully understood. Here we present ext ensions of our previous investigations of the exploitation of higher-order statistics by nonlinear neurons. We use multivariate wavelet statistics to demonstrate that a strictly linear processing would inevitably leave substa ntial statistical dependencies between the outputs of the units. We then co nsider how the basic nonlinearities of cortical neurons-gain control and ON /OFF half-wave rectification-can exploit these higher-order statistical dep endencies. We first show that gain control provides an adaptation to the po lar separability of the multivariate probability density function (PDF), an d, together with an output nonlinearity, enables an overcomplete sparse cod ing. We then consider how the remaining higher-order dependencies between d ifferent units can be exploited by a combination of basic ON/OFF point nonl inearities and subsequent weighted linear combinations. We consider two sta tistical optimization schemes for the computation of the optimal weights: p rincipal component analysis (PCA) and independent component analysis (ICA). Since the intermediate nonlinearities transform some of the higher-order d ependencies into second-order dependencies even the basic PCA approach is a ble to exploit part of the redundancies. ICA ignores this second-order stru cture, but can exploit higher-order dependencies. Both schemes yield a vari ety of nonlinear units which comprise the typical nonlinear processing prop erties, such as end-stopping, side-stopping, complex-cell properties and ex tra-classical receptive field properties, but the 'ideal' complex cells see m only to occur with PCA. Thus, a combination of ON/OFF nonlinearities with an integrated PCA-ICA strategy seems necessary to exploit the statistical proper-ties of natural images.