Faculty Bibliography

The local statistical properties of photographic images, when represented in a multi-scale basis, have been described using Gaussian scale mixtures. Here, we use this local description as a substrate for constructing a global field of Gaussian scale mixtures (FoGSMs). Specifically, we model multi-scale subbands as a product of an exponentiated homogeneous Gaussian Markov random field (hGMRF) and a second independent hGMRF. We show that parameter estimation for this model is feasible, and that samples drawn from a FoGSM model have marginal and joint statistics similar to subband coefficients of photographic images. We develop an algorithm for removing additive Gaussian white noise based on the FoGSM model, and demonstrate denoising performance comparable with state-of-the-art methods

We develop a statistical model to describe the spatially varying behavior of local neighborhoods of coefficients in a multiscale image representation. Neighborhoods are modeled as samples of a multivariate Gaussian density that are modulated and rotated according to the values of two hidden random variables, thus allowing the model to adapt to the local amplitude and orientation of the signal. A third hidden variable selects between this oriented process and a nonoriented scale mixture of Gaussians process, thus providing adaptability to the local orientedness of the signal. Based on this model, we develop an optimal Bayesian least squares estimator for denoising images and show through simulations that the resulting method exhibits significant improvement over previously published results obtained with Gaussian scale mixtures

We propose an efficient methodology for comparing computational models of a perceptually discriminable quantity. Rather than comparing model responses to subjective responses on a set of pre-selected stimuli, the stimuli are computer-synthesized so as to optimally distinguish the models. Specifically, given two computational models that take a stimulus as an input and predict a perceptually discriminable quantity, we first synthesize a pair of stimuli that maximize/minimize the response of one model while holding the other fixed. We then repeat this procedure, but with the roles of the two models reversed. Subjective testing on pairs of such synthesized stimuli provides a strong indication of the relative strengths and weaknesses of the two models. Specifically, the model whose extremal stimulus pairs are easier for subjects to discriminate is the better model. Moreover, careful study of the synthesized stimuli may suggest potential ways to improve a model or to combine aspects of multiple models. We demonstrate the methodology for two example perceptual quantities: contrast and image quality

Statistical dependencies in the responses of sensory neurons govern both the amount of stimulus information conveyed and the means by which downstream neurons can extract it. Although a variety of measurements indicate the existence of such dependencies, their origin and importance for neural coding are poorly understood. Here we analyse the functional significance of correlated firing in a complete population of macaque parasol retinal ganglion cells using a model of multi-neuron spike responses. The model, with parameters fit directly to physiological data, simultaneously captures both the stimulus dependence and detailed spatio-temporal correlations in population responses, and provides two insights into the structure of the neural code. First, neural encoding at the population level is less noisy than one would expect from the variability of individual neurons: spike times are more precise, and can be predicted more accurately when the spiking of neighbouring neurons is taken into account. Second, correlations provide additional sensory information: optimal, model-based decoding that exploits the response correlation structure extracts 20% more information about the visual scene than decoding under the assumption of independence, and preserves 40% more visual information than optimal linear decoding. This model-based approach reveals the role of correlated activity in the retinal coding of visual stimuli, and provides a general framework for understanding the importance of correlated activity in populations of neurons

Image denoising methods are often designed to minimize mean-squared error (MSE) within the subbands of a multiscale decomposition. However, most high-quality denoising results have been obtained with overcomplete representations, for which minimization of MSE in the subband domain does not guarantee optimal MSE performance in the image domain. We prove that, despite this suboptimality, the expected image-domain MSE resulting from applying estimators to subbands that are made redundant through spatial replication of basis functions (e.g., cycle spinning) is always less than or equal to that resulting from applying the same estimators to the original nonredundant representation. In addition, we show that it is possible to further exploit overcompleteness by jointly optimizing the subband estimators for image-domain MSE. We develop an extended version of Stein's unbiased risk estimate (SURE) that allows us to perform this optimization adaptively, for each observed noisy image. We demonstrate this methodology using a new class of estimator formed from linear combinations of localized 'bump' functions that are applied either pointwise or on local neighborhoods of subband coefficients. We show through simulations that the performance of these estimators applied to overcomplete subbands and optimized for image-domain MSE is substantially better than that obtained when they are optimized within each subband. This performance is, in turn, substantially better than that obtained when they are optimized for use on a nonredundant representation