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

How do observers detect the presence of objects or features in visual images? Stochastic stimuli (for example, white noise) have become popular choices for providing a linear characterization of early sensory mechanisms. A recent paper by Neri and Heeger takes this type of methodology a step further, and succeeds in isolating and characterizing non-linear mechanisms responsible for the detection and identification of a specific visual target

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