Redundant populations of simple cells represent wavelet coefficients in monkey V1

Abstract

An analysis of the distribution, H(f), of the preferred spatial frequency (SF) of ∼200 simple cells (SC) in monkey as measured by J. Cavanaugh and T. Movshon illustrates how the sparse wavelet decomposition of an image is represented by a highly redundant population code in V1.

A strong dependence of the distribution H(f) upon the eccentricity E at which the SC receptive fields are centered can be removed by rescaling f by the local Nyquist SF f_Nyq(E) = 1/0.02(E+1.3), resulting in the normalized SF, q(f,E) = f/f_Nyq(E), eq(1).

A model based on the number of neurons being proportional to the signal to noise ratio (SNR) of the wavelet coefficients and a modified 1/f² power spectrum of natural images leads to H(q) ∼ q²/(q²+q₀²)exp(−q²/2s²), using octave bin widths, eq(2).

The low SF cutoff parameter q₀ arises from the finite distance over which the retinal ganglion cell inputs can be pooled in V1. Its estimated value of 0.03–0.05 corresponds to a radius of 2.5–5mm of cortex, or a radius of 1/2 E degrees centered at eccentricity E. The high SF cutoff parameter arises from the spatial filtering in the retina that enforces the Nyquist sampling theorem. Its estimated value of 3.5–4.5 is consistent with size of the center spatial filter of the retinal P cells when scaled by eq (1). H(q) spans 6 octaves with almost all the SCs lying within the central 2–3 octaves. Having only 2–3 SF channels may explain the difficulty of finding maps of SF magnitude with optical techniques. The redundancy of simple cells to wavelet coefficients at the peak of H(q) is at least 100 leading to a SNR of ∼100:1, which is consistent with the peak sensitivity of the MTF lying ∼3 octaves below the SF limit of the visual system.

In summary, the majority of the information in V1 resides at low SFs that is pooled from 100s of ganglion cells, and hardly any information is at the highest SFs. Thus, both the retina and visual cortex utilize highly redundant population codes, not sophisticated spike codes of individual neurons.

Footnotes

 Supported by the Mathers Foundation and the McDonnell Center for Higher Brain Function