Faculty Bibliography

It is widely believed that visual systems are optimized for the visual properties of the environment inhabited by the organism. A specific instance of this principle is known as the Efficient Coding Hypothesis, which holds that the purpose of early visual processing is to produce an efficient representation of the incoming visual signal. The theory provides a quantitative link between the statistical properties of the world and the structure of the visual system. As such, specific instances of this theory have been tested experimentally, and have been used to motivate and constrain models for early visual processing

We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error

Most neurons in macaque area MT (V5) respond vigorously to stimuli moving in a preferred direction, and are suppressed by motion in the opposite direction. The excitatory inputs come from specific groups of directionally selective neurons in lower-order areas, but the inhibitory signals are not so well understood. Some models (e.g. Simoncelli and Heeger, 1998, Vision Res) assume that these signals are pooled across the receptive field, but Qian et al. (1994, J Neurosci) suggested instead that inhibitory inputs interact with excitatory ones only within local regions of space. To explore the location and direction specificity of interactions between MT receptive field subregions, we stimulated small areas of the receptive field with Gabor patches drifting in the preferred direction. We presented these alone and in combination with stimuli drifting in non-preferred directions so that we could study inhibitory signals against background firing elevated by preferred stimuli. Non-preferred gratings suppressed responses strongly when they were presented in the same retinal location as the preferred grating. When the two gratings were separated, suppression was much reduced and was no larger than the suppression of spontaneous firing produced by a non-preferred stimulus presented alone. Our results show that non-preferred stimuli can only inhibit responses generated by excitatory stimuli from nearby regions of space; this suggests that direction-specific inhibition acts within spatially localized subregions of the receptive field. The results can be described by a model in which local excitation and inhibition are combined and rectified before a final stage of spatial pooling.

The pattern of local image velocities on the retina encodes important environmental information. Although humans are generally able to extract this information, they can easily be deceived into seeing incorrect velocities. We show that these 'illusions' arise naturally in a system that attempts to estimate local image velocity. We formulated a model of visual motion perception using standard estimation theory, under the assumptions that (i) there is noise in the initial measurements and (ii) slower motions are more likely to occur than faster ones. We found that specific instantiation of such a velocity estimator can account for a wide variety of psychophysical phenomena

Spike-triggered average (reverse correlation) techniques are effective for linear characterization of neural responses. But cortical neurons exhibit striking nonlinear behaviors that are not captured by such analyses. Many of these nonlinear behaviors are consistent with a gain control (divisive normalization) model. We develop a spike-triggered covariance method for recovering the parameters of such a model. We assume a specific form of normalization, in which spike rate is determined by the half wave-rectified and squared response of a linear kernel divided by the weighted sum of squared responses of linear kernels at different positions, orientations, and spatial frequencies. The method proceeds in two steps. First, the linear kernel of the numerator is estimated using traditional spike-triggered averaging. Second, we measure responses with the excitation of the numerator kernel held constant (this is accomplished by stimulus design, or during data analysis) but with random excitation along all other axes. We construct a covariance matrix of the stimuli eliciting a spike, and perform a principal components decomposition of this matrix. The principal axes (eigenvectors) correspond to the directions in which the response of the neuron is modulated divisively. The variance along each axis (eigenvalue) is monotonically decreasing as a function of strength of suppression along that axis. The kernels and weights of an equivalent normalization model may be estimated from these eigenvalues and eigenvectors. We demonstrate through simulation that the technique yields a good estimate of the model parameters, and we examine accuracy as a function of the number of spikes. This method provides an opportunity to test a normalization model experimentally, by first estimating model parameters for an individual neuron, and then examining the ability of the resulting model to account for responses of that neuron to a variety of other stimuli.