Higher Order Whitening of Natural Images

Natural images are approximately scale invariant resulting in long range statistical regularities that typically obey a power law. For example, images have considerable regularity in their second order spatial correlations as measured by the power spectrum. Processing images to remove these expected correlations is known as whitening an image. Because the expected value of the power spectrum has a regular form (a power law) linear processing such as convolution can be used to whiten an image. After whitening an image, higher order regularities that cannot be removed with linear processing still exist in the form of correlations in the magnitude. In this paper it is shown that these correlations also obey a power law and a non-linear method is used to remove them, a process referred to as higher order whitening. The method is invertible demonstrating that while redundancy is removed no information is lost. Experiments are given showing that after higher order whitening the coefficients can be severely quantized yet a good reconstruction is possible despite the nonlinearities.