Extensions of independent component analysis for natural image data

An understanding of the statistical properties of natural images is useful for any kind of processing to be performed on them. Natural image statistics are, however, in many ways as complex as the world which they depict. Fortunately, the dominant low-level statistics of images are sufficient for many different image processing goals. A lot of research has been devoted to second order statistics of natural images over the years. Independent component analysis is a statistical tool for analyzing higher than second order statistics of data sets. It attempts to describe the observed data as a linear combination of independent, latent sources. Despite its simplicity, it has provided valuable insights of many types of natural data. With natural image data, it gives a sparse basis useful for efficient description of the data. Connections between this description and early mammalian visual processing have been noticed. The main focus of this work is to extend the known results of applying independent component analysis on natural images. We explore different imaging techniques, develop algorithms for overcomplete cases, and study the dependencies between the components by using a model that finds a topographic ordering for the components as well as by conditioning the statistics of a component on the activity of another. An overview is provided of the associated problem field, and it is discussed how these relatively small results may eventually be a part of a more complete solution to the problem of vision.