Nonlinear Source Separation

The purpose of this lecture book is to present the state of the art in nonlinear blind source separation, in a form appropriate for students, researchers and developers. Source separation deals with the problem of recovering sources that are observed in a mixed condition. When we have little knowledge about the sources and about the mixture process, we speak of blind source separation. Linear blind source separation is a relatively well studied subject, however nonlinear blind source separation is still in a less advanced stage, but has seen several significant developments in the last few years. This publication reviews the main nonlinear separation methods, including the separation of post-nonlinear mixtures, and the MISEP, ensemble learning and kTDSEP methods for generic mixtures. These methods are studied with a significant depth. A historical overview is also presented, mentioning most of the relevant results, on nonlinear blind source separation, that have been presented over the years.

Introduction.- Linear Source Separation.- Nonlinear Separation.- Final Comments.- Statistical Concepts.- Online Software and Data.

Luis B. Almeida is a full professor of Signals and Systems, and of Neural Networks and Machine Learning, at Instituto Superior Tecnico, Technical University of Lisbon, and a researcher at the Telecommunications Institute, Lisbon, Portugal. He holds a Ph. D. in Signal Processing from the Technical University of Lisbon. He has formerly taught Systems Theory, Telecommunications, Digital Systems and Mathematical Analysis, among others. Luis B. Almeida's current research focuses on nonlinear source separation. Formerly he has performed research on speech modeling and coding, Fourier and time-frequency analysis of signals, and training algorithms for neural networks. Some highlights of his work include the sinusoidal model for voiced speech, currently in use in INMARSAT and IRIDIUM telephones (developed with F.M. Silva and J.S. Marques), work on the Fractional Fourier Transform, the development of recurrent backpropagation, and the development of the MISEP method of nonlinear source separation. Luis B. Almeida has been a founding Vice-President of the European Neural Network Society and the founding President of INESC-ID (a nonprofit research institute associated with the Technical University of Lisbon).