Faculty Bibliography

We develop a new class of non-Gaussian multiscale stochastic processes defined by random cascades on trees of wavelet or other multiresolution coefficients. These cascades reproduce a rich semi-parametric class of random variables known as Gaussian scale mixtures. We demonstrate that this model class can accurately capture the remarkably regular and non-Gaussian features of natural images in a parsimonious fashion, involving only a small set of parameters. In addition, this model structure leads to efficient algorithms for image processing. In particular, we develop a Newton-like algorithm for MAP estimation that exploits very fast algorithms for linear-Gaussian estimation on trees, and hence is efficient. On the basis of this MAP estimator, we develop and illustrate a denoising technique that is based on a global prior model, and preserves the structure of natural images (e.g., edges). © 2000 SPIE--The International Society for Optical Engineering.

Visual motion is processed by neurons in primary visual cortex that are sensitive to spatial orientation and speed. Many models of local velocity computation are based on a second stage that pools the outputs of first-stage neurons selective for different orientations, but the nature of this pooling remains controversial. In a human psychophysical detection experiment, we found near-perfect summation of image energy when it was distributed uniformly across all orientations, but poor summation when it was concentrated in specific orientation bands. The data are consistent with a model that integrates uniformly over all orientations, even when this strategy is sub-optimal