Image processing using ICA: a new perspective

Abstract

Independent component analysis (ICA) provides a sparse representation of natural images in terms of a set of oriented bases. So far, the interest on this result lay on its apparent connection to the neural processing of the mammalian primary visual cortex. In this paper we provide an analysis from a formal (not physiological) point of view. We show that ICA of a natural image is equivalent to filtering the image using a high-pass filter, followed by a sampling. This result determines, on the one hand, the sparse distribution of the independent components and, on the other hand, that the image bases resemble "edges" of the original image. Some experiments are included to illustrate the theoretical conclusions