CHAPTER 4
Independent Component Analysis
Stefan A. Robila
4.1
Introduction
Independent component analysis (lCA) is a multivariate data analysis method
that, given a linear mixture of statistical independent sources, recovers these
components by producing an unmixing matrix. Stemming from a more general
problem called blind source separation (BSS), ICA has become increasingly
popular in recent years with several excellent books (e. g. Cichocki and Amari
2002; Haykin 2000; Hyvarinen et al. 2001) and a large number of papers being
published. Its attractiveness is explained by its relative simplicity as well as from
a large number of application areas (Haykin 2000). For example, ICA has been
successfully employed in sound separation (Lee 1998), financial forecasting
(Back and Weingend 1997), biomedical data processing (Lee 1998), image
filtering (Cichocki and Amari 2002), and remote sensing (Tu et al. 2001).
While in many of these applications, the problems do not exactly fit the required
setting, ICA based algorithms have been shown to be robust enough to produce
accurate solutions. In fact, it is this robustness that has fueled the theoretical
advances in this area (Haykin 2000).
In view of such success, and given the fact that hyperspectral data can be
modeled as multivariate data, it is natural to examine how ICA can be used to
process hyperspectral images. This chapter provides an overview of ICA and
its application to the processing of hyperspectral images. The ICA concept is
introduced in Sect. 4.2 followed by the description of some of the most popular
algorithms. Finally, in the last section, a few applications are presented.
4.2
Concept of ICA
Consider a cocktail party in a room in which several persons are talking to each
other. When they talk at the same time, their voices cannot be distinguished
even with the help of several microphones. This is because the recorded sound
signals will be mixtures of the source sound signals (voices). The exact manner
in which the voices have been mixed is unknown and may depend on the
distance from the microphone and other factors. We are, thus, faced with
P. K. Varshney et al., Advanced Image Processing Techniques for Remotely Sensed Hyperspectral Data
© Springer-Verlag Berlin Heidelberg 2004
Independent Component Analysis
Stefan A. Robila
4.1
Introduction
Independent component analysis (lCA) is a multivariate data analysis method
that, given a linear mixture of statistical independent sources, recovers these
components by producing an unmixing matrix. Stemming from a more general
problem called blind source separation (BSS), ICA has become increasingly
popular in recent years with several excellent books (e. g. Cichocki and Amari
2002; Haykin 2000; Hyvarinen et al. 2001) and a large number of papers being
published. Its attractiveness is explained by its relative simplicity as well as from
a large number of application areas (Haykin 2000). For example, ICA has been
successfully employed in sound separation (Lee 1998), financial forecasting
(Back and Weingend 1997), biomedical data processing (Lee 1998), image
filtering (Cichocki and Amari 2002), and remote sensing (Tu et al. 2001).
While in many of these applications, the problems do not exactly fit the required
setting, ICA based algorithms have been shown to be robust enough to produce
accurate solutions. In fact, it is this robustness that has fueled the theoretical
advances in this area (Haykin 2000).
In view of such success, and given the fact that hyperspectral data can be
modeled as multivariate data, it is natural to examine how ICA can be used to
process hyperspectral images. This chapter provides an overview of ICA and
its application to the processing of hyperspectral images. The ICA concept is
introduced in Sect. 4.2 followed by the description of some of the most popular
algorithms. Finally, in the last section, a few applications are presented.
4.2
Concept of ICA
Consider a cocktail party in a room in which several persons are talking to each
other. When they talk at the same time, their voices cannot be distinguished
even with the help of several microphones. This is because the recorded sound
signals will be mixtures of the source sound signals (voices). The exact manner
in which the voices have been mixed is unknown and may depend on the
distance from the microphone and other factors. We are, thus, faced with
P. K. Varshney et al., Advanced Image Processing Techniques for Remotely Sensed Hyperspectral Data
© Springer-Verlag Berlin Heidelberg 2004