Is sparse and distributed the coding goal of simple cells?

The question of why the receptive fields of simple cells in the primary visual cortex are Gabor-like is a crucial one in vision research. Many research efforts (Olshausen and Field 1996, 1997; van Hateren and Ruderman 1998; van Hateren and van der Schaaf 1998) that yield a set of localized, oriented, and bandpass Gabor-like receptive fields believe that sparse and distributed is the coding goal of simple cells. This paper investigates a more general coding strategy that measures equally any departure from normality in the simple cells' responses. That is, we investigate the possibility that highly kurtotic response histograms may result if simple cells explicitly seek, not maximally kurtotic, but rather maximally non-Gaussian response histograms to natural images. It is found that, under this coding strategy, the simulations produce a majority of localized, oriented, bandpass (Gabor-like) receptive fields. Some receptive fields, however, are spatially distributed and show little oriented structure. Nearly all receptive fields, regardless of whether they are Gabor-like or non-Gabor-like, yield highly kurtotic response histograms to natural images. Thus, in seeking maximally non-Gaussian response histograms, receptive fields spontaneously yield highly kurtotic histograms. The presence in our ensemble of nonlocalized, nonoriented receptive fields may be due to the artificial requirement that receptive fields be orthonormal. We conclude that the high kurtoses observed in the response histograms of simple-cell receptive fields to natural images may reflect a property of natural images themselves rather than an explicit coding goal used to structure simple-cell receptive fields.