Hyperspectral Data Processing: Algorithm Design and Analysis

6.2 Dimensionality Reduction by Second-Order Statistics-Based Component Analysis Transforms

A CA transform generally transforms the image data into a set of data components so that the correlation among the transformed data components is uncorrelated according to a criterion. More specifically, a component transform represents a data space by a set of its generated data components. Two second-order component transforms have been widely used in remote sensing image processing, which are variance-based PCA transforms and SNR-based transforms and discussed as follows.

6.2.1 Eigen Component Analysis Transforms

The simplest eigen-CA transforms are those based on data variance. PCA represents this type of data variance-based CA transforms.

6.2.1.1 Principal Components Analysis

The principal components analysis (PCA), also known as Hotelling transform (Gonalez and Woods, 2002) as well as principal components transformation (PCT) (Richards and Jia, 1999; Schowengerdt, 1997), is an optimal transform to represent data in the sense of data variance. It can be considered as a discrete time version of the Karhunen–Loeve transform (KLT) in signal processing and communications (Poor, 1994) that is an optimal transform using eigenfunctions as basis functions to represent and de-correlate a function in the sense of mean-squared error. It is generally referred to as Karhunen–Loeve expansion that represents a function as a series in terms of eigenfunctions where these eigenfunctions are continuous-time ...