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By examining the experimental data on the statistical properties of natural scenes together with (retinal) contrast sensitivity data, we arrive at a first principle, theoretical hypothesis for the purpose of retinal processing and its relationship to an animal's environment. We argue that the retinal goal is to transform the visual input as much as possible into a statistically independent basis as the first step in creating a redundancy reduced representation in the cortex, as suggested by Barlow. The extent of this whitening of the input is limited, however, by the need to suppress input noise. Our explicit theoretical solutions for the retinal filters also show a simple dependence on mean stimulus luminance: they predict an approximate Weber law at low spatial frequencies and a De Vries-Rose law at high frequencies. Assuming that the dominant source of noise is quantum, we generate a family of contrast sensitivity curves as a function of mean luminance. This family is compared to psychophysical data.

We propose a theory of the early processing in the mammalian visual pathway. The theory is formulated in the language of information theory and hypothesizes that the goal of this processing is to recode in order to reduce a “generalized redundancy” subject to a constraint that specifies the amount of average information preserved. In the limit of no noise, this theory becomes equivalent to Barlow's redundancy reduction hypothesis, but it leads to very different computational strategies when noise is present. A tractable approach for finding the optimal encoding is to solve the problem in successive stages where at each stage the optimization is performed within a restricted class of transfer functions. We explicitly find the solution for the class of encodings to which the parvocellular retinal processing belongs, namely linear and nondivergent transformations. The solution shows agreement with the experimentally observed transfer functions at all levels of signal to noise.

A recent computational theory suggests that visual processing in the retina and the lateral geniculate nucleus (LGN) serves to recode information into an efficient form (Atick and Redlich, 1990). Information theoretic analysis showed that the representation of visual information at the level of the photoreceptors is inefficient, primarily attributable to a high degree of spatial and temporal correlation in natural scenes. It was predicted, therefore, that the retina and the LGN should recode this signal into a decorrelated form or, equivalently, into a signal with a "white" spatial and temporal power spectrum. In the present study, we tested directly the prediction that visual processing at the level of the LGN temporarily whitens the natural visual input. We recorded the responses of individual neurons in the LGN of the cat to natural, time-varying images (movies) and, as a control, to white-noise stimuli. Although there is substantial temporal correlation in natural inputs (Dong and Atick, 1995b), we found that the power spectra of LGN responses were essentially white. Between 3 and 15 Hz, the power of the responses had an average variation of only +/-10.3%. Thus, the signals that the LGN relays to visual cortex are temporarily decorrelated. Furthermore, the responses of X-cells to natural inputs can be well predicted from their responses to white-noise inputs. We therefore conclude that whitening of natural inputs can be explained largely by the linear filtering properties (Enroth-Cugell and Robson, 1966). Our results suggest that the early visual pathway is well adapted for efficient coding of information in the natural visual environment, in agreement with the prediction of the computational theory.

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