The responses of simple cells in primary visual cortex to sinusoidal gratings can primarily be predicted from their spatial receptive fields, as mapped using spots or bars. Although this quasilinearity is well documented, it is not clear whether it holds for complex natural stimuli. We recorded from simple cells in the primary visual cortex of anesthetized ferrets while stimulating with flashed digitized photographs of natural scenes. We applied standard reverse-correlation methods to quantify the average natural stimulus that invokes a neuronal response. Although these maps cannot be the receptive fields, we find that they still predict the preferred orientation of grating for each cell very well (r = 0.91); they do not predict the spatial-frequency tuning. Using a novel application of the linear reconstruction method called regularized pseudoinverse, we were able to recover high-resolution receptive-field maps from the responses to a relatively small number of natural scenes. These receptive-field maps not only predict the optimum orientation of each cell (r = 0.96) but also the spatial-frequency optimum (r = 0.89); the maps also predict the tuning bandwidths of many cells. Therefore, our first conclusion is that the tuning preferences of the cells are primarily linear and constant across stimulus type. However, when we used these maps to predict the actual responses of the cells to natural scenes, we did find evidence of expansive output nonlinearity and nonlinear influences from outside the classical receptive fields, orientation tuning, and spatial-frequency tuning.

We have examined the spatial-frequency selectivity of neurons in areas 17 and 18 of the adult pigmented ferret, by measuring how the amplitude of response depends on the spatial-frequency of moving sinusoidal gratings of optimal orientation and fixed contrast. Neurons in area 17 of the ferret respond optimally to low spatial frequencies [average 0.25 cycles per degree (c/deg)], much lower than the optima for cat area 17. The tuning curves are of the same form as those found in cat and monkey: unimodal with bandwidths in the range 0.8-3.5 octaves. Neurons in area 18 of the ferret respond optimally to even lower spatial frequencies (average 0.087 c/deg) than area 17 neurons, and the distributions of optimal spatial frequency for areas 17 and 18 hardly overlap. In both cortical areas, the bandwidth of the tuning curves is inversely correlated with optimal spatial frequency. This marked difference in tuning between the two cortical areas is probably attributable to differential geniculo-cortical projections. Small injections of fluorescent latex microspheres or horseradish peroxidase (HRP) were made into area 17 or area 18 in order to investigate the populations of geniculate neurons projecting to the two cortical areas. After injections into area 17, labelled neurons are found predominantly in the geniculate A layers, with a few neurons labelled in the C layers. Conversely, after an area 18 injection, similar numbers of labelled neurons are found in the C layers as in the A layers. Soma-size analysis of the neurons in the A-layers suggests the existence of two populations of relay neurons, which project differentially to areas 17 and 18. The different geniculate inputs and the different spatial-frequency tuning in areas 17 and 18 may imply that the two cortical areas process visual information more in parallel than in series.

Visual experience before eye-opening is not usually thought to have any developmental significance. Here we show that naturalistic visual stimuli presented through unopened eyelids robustly activate neurons in the ferret dorsal lateral geniculate nucleus. Further, dark-rearing prior to natural eye-opening has striking effects upon geniculate physiology. Receptive field maps after dark-rearing show increased convergence of On- and Off-center responses, and neurons frequently respond to both bright and dark phases of drifting gratings. There is also increased selectivity for the orientation of the gratings. These abnormalities of On-Off segregation can be explained by the finding that the responses of immature On and Off cells to naturalistic stimuli are strongly anticorrelated.

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Various arguments suggest that neuronal coding of natural sensory stimuli should be sparse (i.e., individual neurons should respond rarely but should respond reliably). We examined sparseness of visual cortical neurons in anesthetized ferret to flashed natural scenes. Response behavior differed widely between neurons. The median firing rate of 4.1 impulses per second was slightly higher than predicted from consideration of metabolic load. Thirteen percent of neurons (12 of 89) responded to Ͻ5% of the images, but one-half responded to Ͼ25% of images. Multivariate analysis of the range of sparseness values showed that 67% of the variance was accounted for by differing response patterns to moving gratings. Repeat presentation of images showed that response variance for natural images exaggerated sparseness measures; variance was scaled with mean response, but with a lower Fano factor than for the responses to moving gratings. This response variability and the "soft" sparse responses (Rehn and Sommer, 2007) raise the question of what constitutes a reliable neuronal response and imply parallel signaling by multiple neurons. We investigated whether the temporal structure of responses might be reliable enough to give additional information about natural scenes. Poststimulus time histogram shape was similar for "strong" and "weak" stimuli, with no systematic change in first-spike latency with stimulus strength. The variance of first-spike latency for repeat presentations of the same image was greater than the latency variance between images. In general, responses to flashed natural scenes do not seem compatible with a sparse encoding in which neurons fire rarely but reliably.

Recent studies have recovered receptive-field maps of simple cells in visual cortex from their responses to natural scene stimuli. Natural scenes have many theoretical and practical advantages over traditional, artificial stimuli; however, the receptive-field estimation methods are more complex than for white-noise stimuli. Here, we describe and justify several of these methods-spectral correction of the reverse correlation estimate, direct least-squares solution, iterative least-squares algorithms and regularized least-squares solutions. We investigate the pros and cons of the different methods, and evaluate them in a head-to-head comparison for simulated simple-cell data. This shows that, at least for quasilinear simulated simple cells, a regularized solution ('reginv') is most efficient, requiring fewer stimulus presentations for high-resolution reconstruction of the first-order kernel. We also investigate several practical issues that determine the success of this kind of experiment-the effects of neuronal nonlinearities, response variability and the choice of stimulus regime.

The aim of this paper is to show how information theoretic measures can be used to analyse and interpret the results of psychophysical experiments designed to search for conditions under which information from one source modulates the transmission of information from another source. We therefore use measures of mutual and conditional information to analyse systems with two inputs. The information transmitted by such a system can be split into three components depending on whether it is shared between the two inputs or is specific to each. We are concerned here with distinguishing systems that use one input to modulate transmission of information about the other from systems that simply add both inputs, and show how the three components provide evidence for distinguishing between additive and modulatory effects. We also report numerical simulations of the sampling biasses and variances of these measures as a function of the sample size and propose minimum sample sizes that should be used to overcome the bias.

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