Washington University School of Medicine
Population Coding in V1
Tuesday 11th of April 2006 at 05:00pm
With population codes, the number of neurons is proportional to the signal to noise ratio (SNR) of each degree of freedom they represent. This hypothesis allows one to use the measured distribution of the preferred spatial frequencies (SFs) of cells in V1 to quantify how SF information is transmitted down the optic nerve and represented in V1. This work describes the results of such an analysis on several hundred monkey simple and complex cells measured by J. Cavanaugh and W. Bair in the Movshon lab. This SNR analysis explains a long outstanding question as to why the preferred SFs of most cells in V1 lie far below the highest SF provided by the ganglion cells, while almost all the coefficients in a wavelet decomposition of an image reside at the highest SFs. Qualitatively, the answer is that there is much more power at low SFs because of the 1/f^2 power spectrum of natural images and so more neurons are allocated to represent the high SNR available at low SFs. This analysis quantifies how the ganglion cells are organized to transmit the high SNR available at low SFs using a highly redundant coding scheme, rather than being decorrelated by "whitening" spatial filters. The redundancy of the representation within V1 is found to be on the order of 100 neurons per wavelet coefficient at low SFs relative to the redundancy at the highest SFs, in conflict with the sparse coding hypothesis. A typical simple cell in V1 gets inputs from ~1000 ganglion cells pooled over a radius of 2-3mm, which is large compared to the 1mm prototypical Hubel and Weisel cortial column (see also ). In addition, the distribution of the preferred SFs of complex cells is shifted to higher SFs relative to that of simple cells by almost an octave, suggesting complex cells may not get their inputs from simple cells. In summary, this engineering analysis quantifies the way V1 cells participate in population codes to represent a much lower dimensional space, which adds to the growing weight of evidence that population codes are the primary way neuronal systems represent and process information .
 Cavanaugh JR, Bair W, and Movshon JA (2002), Selectivity and spatial distribution of signals from the receptive field surround in macaque V1 neurons, J Neurophysiol. 88: 2547-56.
 Eliasmith C, and Anderson CH (2003), "Neural Engineering", MIT Press.
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