Principal Components and Whitening

Abstract

The most classical method of analyzing the statistical structure of multi-dimensional random data is principal component analysis (PCA), which is also called the Karhunen--Loève transformation, or the Hotelling transformation. In this chapter, we will consider the application of PCA to natural images. It will be found that it is not a successful model in terms of modeling the visual system. However, PCA provides the basis for all subsequent models. In fact, before applying the more successful models described in the following chapters, PCA is often applied as a preprocessing of the data. So, the investigation of the statistical structure of natural images must start with PCA.