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Abstract

It has long been assumed that sensory neurons are adapted, through both evolutionary and developmental processes, to the statistical properties of the signals to which they are exposed. In particular, Attneave (1954) and Barlow (1961) proposed that redundancy reduction could provide a link between environmental statistics and neural responses in a similar spirit to projection pursuit density estimation. A striking result related to this view is that three key features of V1 simple cell receptive fields – localization, bandpass filtering, and orientation selectivity – emerge if one maximizes statistical independence (i.e. minimizes the redundancy) of linear filters in response to natural images with an algorithm known as Independent Component Analysis (ICA). In addition, also the nonlinear filter property of divisive normalization has been interpreted as a mechanism for redundancy reduction. In order to quantitatively assess the potential of these prominent neural response properties for modeling the statistics of natural images we evaluate their relative contribution to the total amount of redundancy reduction. We find that bandpass filtering has the largest potential for redundancy reduction, followed by divisive normalization. Localization and orientation selectivity turn out to have only a surprisingly small potential for redundancy reduction. We conclude that the common model for V1 simple cells is not flexible enough to implement significantly more knowledge about the statistics of natural images than what can already be modeled at the level of the retina.