Independent Component Analysis (ICA) is one of the most exciting new topics in fields such as neural networks, advanced statistics, and signal processing. This is the first book to provide a comprehensive introduction to this new technique complete with the fundamental mathematical background needed to understand and utilize it. It offers a general overview of the basics of ICA, important solutions and algorithms, and in-depth coverage of new applications in image processing, telecommunications, audio signal processing, and more.

Independent Component Analysis is divided into four sections that cover:

• General mathematical concepts utilized in the book
• The basic ICA model and its solution
• Various extensions of the basic ICA model
• Real-world applications for ICA models

Contents:

• Preface
• Introduction
• MATHEMATICAL PRELIMINARIES
• Random Vectors and Independence
• Gradients and Optimisation Methods
• Estimation Theory
• Information Theory
• Principal Component Analysis and Whitening
• BASIC INDEPENDENT COMPONENT ANALYSIS
• What is Independent Component Analysis?
• ICA by Maximization of Nongaussianity
• ICA by Maximum Likelihood Estimation
• ICA by Minimization of Mutual Information
• ICA by Tensorial Methods
• ICA by Nonlinear Decorrelation and Nonlinear PCA
• Practical Considerations
• Overview and Comparison of Basic ICA Methods
• EXTENSIONS AND RELATED METHODS
• Noisy ICA
• ICA with Overcomplete Bases
• Nonlinear ICA
• Methods using Time Structure
• Convolutive Mixtures and Blind Deconvolution
• Other Extensions
• APPLICATIONS OF ICA
• Feature Extraction by ICA
• Brain Imaging Applications
• Telecommunications
• Other Applications
• References
• Index