Introduction -- Expressions and variants of the linear-quadratic mixing model -- Invertibility of mixing model, separating structures -- Independent component analysis and Bayesian separation methods -- Matrix factorization methods -- Sparse component analysis methods -- Extensions and conclusion -- Bilinear Sparse Component Analysis methods based on single source zones -- Conclusion.

This book provides a detailed survey of the methods that were recently developed to handle advanced versions of the blind source separation problem, which involve several types of nonlinear mixtures. Another attractive feature of the book is that it is based on a coherent framework. More precisely, the authors first present a general procedure for developing blind source separation methods. Then, all reported methods are defined with respect to this procedure. This allows the reader not only to more easily follow the description of each method but also to see how these methods relate to one another. The coherence of this book also results from the fact that the same notations are used throughout the chapters for the quantities (source signals and so on) that are used in various methods. Finally, among the quite varied types of processing methods that are presented in this book, a significant part of this description is dedicated to methods based on artificial neural networks, especially recurrent ones, which are currently of high interest to the data analysis and machine learning community in general, beyond the more specific signal processing and blind source separation communities. Presents advanced configurations of the blind source separation problem, involving bilinear, linear-quadratic and polynomial mixing models; Provides a detailed and coherent description of the methods reported in the literature for handling these types of mixing phenomena; Focuses on complex configurations involving nonlinear mixing transforms.