Here, we eliminate these restrictions, and develop a more general model for information maximization. For a known photoreceptor mosaic, and given a specification of retinal blur, photoreceptor noise, ganglion cell noise, and an image probability model, we can compute the mutual information between the image and the RGC population firing rates. If both noise sources are white and Gaussian, the receptive fields that optimize information transfer may be efficiently computed, and are unique up to an arbitrary orthogonal matrix.

We compare this solution to data recorded in vitro from macaque retina using a large-scale multielectrode. Both cone locations and RGC receptive fields are estimated based on spike-triggered averaging. We analyzed a patch of retina that covers roughly 4 x 8 deg in visual angle at 40 deg eccentricity. We compute the optimal model receptive fields based on the measured cone mosaic, using a natural image data set [Doi et al., 2003], assuming optical blur to be that of humans at the same retinal eccentricity [Navarro et al., 1993], and with noise roughly matched to neural data [Borst and Theunissen 1999]. We select the unconstrained orthogonal matrix so as to minimize the squared error between measured and model receptive fields.

The resulting population of receptive fields is consistent with those estimated for the real cells. They exhibit not only the general position and size of the real cells, but also the remarkably precise "tiling" seen in the real cells, with the idiosyncratic shapes of each individual cell complementing those of their neighbors like interlocking pieces of a jigsaw puzzle. Thus, we conclude that the precise shape and size of individual RGCs, as well as the tiling behaviors of the population, are consistent with the efficient coding hypothesis.