Faculty Bibliography

In this paper, we describe a nonlinear image representation based on divisive normalization that is designed to match the statistical properties of photographic images, as well as the perceptual sensitivity of biological visual systems. We decompose an image using a multi-scale oriented representation, and use Student's t as a model of the dependencies within local clusters of coefficients. We then show that normalization of each coefficient by the square root of a linear combination of the amplitudes of the coefficients in the cluster reduces statistical dependencies. We further show that the resulting divisive normalization transform is invertible and provide an efficient iterative inversion algorithm. Finally, we probe the statistical and perceptual advantages of this image representation by examining its robustness to added noise, and using it to enhance image contrast.

We consider the problem of transforming a signal to a representation in which the components are statistically independent. When the signal is generated as a linear transformation of independent Gaussian or non-Gaussian sources, the solution may be computed using a linear transformation (PCA or ICA, respectively). Here, we consider a complementary case, in which the source is non-Gaussian but elliptically symmetric. Such a source cannot be decomposed into independent components using a linear transform, but we show that a simple nonlinear transformation, which we call radial Gaussianization (RG), is able to remove all dependencies. We apply this methodology to natural signals, demonstrating that the joint distributions of nearby bandpass filter responses, for both sounds and images, are closer to being elliptically symmetric than linearly transformed factorial sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either pairs or blocks of bandpass filter responses is significantly greater than that achieved by PCA or ICA.