Density Modeling of Images using a Generalized Normalization Transformation

TL;DR

This paper presents a parametric nonlinear transformation that Gaussianizes natural image data, enabling effective density modeling, noise removal, and unsupervised deep network optimization.

Contribution

It introduces a novel, differentiable transformation optimized for natural images, outperforming existing methods in Gaussianization and enabling new applications.

Findings

Significantly reduces mutual information between components.

Produces samples visually similar to natural image patches.

Enables noise removal and unsupervised deep network training.

Abstract

We introduce a parametric nonlinear transformation that is well-suited for Gaussianizing data from natural images. The data are linearly transformed, and each component is then normalized by a pooled activity measure, computed by exponentiating a weighted sum of rectified and exponentiated components and a constant. We optimize the parameters of the full transformation (linear transform, exponents, weights, constant) over a database of natural images, directly minimizing the negentropy of the responses. The optimized transformation substantially Gaussianizes the data, achieving a significantly smaller mutual information between transformed components than alternative methods including ICA and radial Gaussianization. The transformation is differentiable and can be efficiently inverted, and thus induces a density model on images. We show that samples of this model are visually similar to samples of natural image patches. We demonstrate the use of the model as a prior probability density that can be used to remove additive noise. Finally, we show that the transformation can be cascaded, with each layer optimized using the same Gaussianization objective, thus offering an unsupervised method of optimizing a deep network architecture.