Density Modeling of Images using a Generalized Normalization Transformation
This work provides a novel density model for natural images that can be used as a prior for tasks like noise removal, though it is incremental in advancing unsupervised deep network optimization.
The authors tackled the problem of modeling the density of natural images by introducing a parametric nonlinear transformation optimized to Gaussianize image data, achieving significantly lower mutual information between transformed components compared to existing methods like ICA and radial Gaussianization.
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.