Handbook of Blind Source Separation

Book Description

Edited by the people who were forerunners in creating the field, together with contributions from 34 leading international experts, this handbook provides the definitive reference on Blind Source Separation, giving a broad and comprehensive description of all the core principles and methods, numerical algorithms and major applications in the fields of telecommunications, biomedical engineering and audio, acoustic and speech processing. Going beyond a machine learning perspective, the book reflects recent results in signal processing and numerical analysis, and includes topics such as optimization criteria, mathematical tools, the design of numerical algorithms, convolutive mixtures, and time frequency approaches. This Handbook is an ideal reference for university researchers, R&D engineers and graduates wishing to learn the core principles, methods, algorithms, and applications of Blind Source Separation.



  • Covers the principles and major techniques and methods in one book
  • Edited by the pioneers in the field with contributions from 34 of the world’s experts
  • Describes the main existing numerical algorithms and gives practical advice on their design
  • Covers the latest cutting edge topics: second order methods; algebraic identification of under-determined mixtures, time-frequency methods, Bayesian approaches, blind identification under non negativity approaches, semi-blind methods for communications
  • Shows the applications of the methods to key application areas such as telecommunications, biomedical engineering, speech, acoustic, audio and music processing, while also giving a general method for developing applications

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. About the editors
  6. Preface
  7. Contributors
  8. Chapter 1. Introduction
    1. 1.1 Genesis of blind source separation
    2. 1.2 Problem formalization
    3. 1.3 Source separation methods
    4. 1.4 Spatial whitening, noise reduction and PCA
    5. 1.5 Applications
    6. 1.6 Content of the handbook
    7. References
  9. Chapter 2. Information
    1. 2.1 Introduction
    2. 2.2 Methods based on mutual information
    3. 2.3 Methods based on mutual information rate
    4. 2.4 Conclusion and perspectives
    5. References
  10. Chapter 3. Contrasts
    1. 3.1 Introduction
    2. 3.2 Cumulants
    3. 3.3 MISO contrasts
    4. 3.4 MIMO contrasts for static mixtures
    5. 3.5 MIMO contrasts for dynamic mixtures
    6. 3.6 Constructing other contrast criteria
    7. 3.7 Conclusion
    8. References
  11. Chapter 4. Likelihood
    1. 4.1 Introduction: Models and likelihood
    2. 4.2 Transformation model and equivariance
    3. 4.3 Independence
    4. 4.4 Identifiability, stability, performance
    5. 4.5 Non-Gaussian models
    6. 4.6 Gaussian models
    7. 4.7 Noisy models
    8. 4.8 Conclusion: A general view
    9. 4.9 Appendix: Proofs
    10. References
  12. Chapter 5. Algebraic methods after prewhitening
    1. 5.1 Introduction
    2. 5.2 Independent component analysis
    3. 5.3 Diagonalization in least squares sense
    4. 5.4 Simultaneous diagonalization of matrix slices
    5. 5.5 Simultaneous diagonalization of third-order tensor slices
    6. 5.6 Maximization of the tensor trace
    7. References
  13. Chapter 6. Iterative algorithms
    1. 6.1 Introduction
    2. 6.2 Model and goal
    3. 6.3 Contrast functions for iterative BSS/ICA
    4. 6.4 Iterative search algorithms: Generalities
    5. 6.5 Iterative whitening
    6. 6.6 Classical adaptive algorithms
    7. 6.7 Relative (natural) gradient techniques
    8. 6.8 Adapting the nonlinearities
    9. 6.9 Iterative algorithms based on deflation
    10. 6.10 The FastICA algorithm
    11. 6.11 Iterative algorithms with optimal step size
    12. 6.12 Summary, conclusions and outlook
    13. References
  14. Chapter 7. Second-order methods based on color
    1. 7.1 Introduction
    2. 7.2 WSS processes
    3. 7.3 Problem formulation, identifiability and bounds
    4. 7.4 Separation based on joint diagonalization
    5. 7.5 Separation based on maximum likelihood
    6. 7.6 Additional issues
    7. References
  15. Chapter 8. Convolutive mixtures
    1. 8.1 Introduction and mixture model
    2. 8.2 Invertibility of convolutive MIMO mixtures
    3. 8.3 Assumptions
    4. 8.4 Joint separating methods
    5. 8.5 Iterative and deflation methods
    6. 8.6 Non-stationary context
    7. References
  16. Chapter 9. Algebraic identification of under-determined mixtures
    1. 9.1 Observation model
    2. 9.2 Intrinsic identifiability
    3. 9.3 Problem formulation
    4. 9.4 Higher-order tensors
    5. 9.5 Tensor-based algorithms
    6. 9.6 Appendix: expressions of complex cumulants
    7. References
  17. Chapter 10. Sparse component analysis
    1. 10.1 Introduction
    2. 10.2 Sparse signal representations
    3. 10.3 Joint sparse representation of mixtures
    4. 10.4 Estimating the mixing matrix by clustering
    5. 10.5 Square mixing matrix: Relative Newton method
    6. 10.6 Separation with a known mixing matrix
    7. 10.7 Conclusion
    8. 10.8 Outlook
    9. Acknowledgements
    10. References
  18. Chapter 11. Quadratic time-frequency domain methods
    1. 11.1 Introduction
    2. 11.2 Problem statement
    3. 11.3 Spatial quadratic spectra and representations
    4. 11.4 Time-frequency points selection
    5. 11.5 Separation algorithms
    6. 11.6 Practical and computer simulations
    7. 11.7 Summary and conclusion
    8. References
  19. Chapter 12. Bayesian approaches
    1. 12.1 Introduction
    2. 12.2 Source separation forward model and notations
    3. 12.3 General Bayesian scheme
    4. 12.4 Relation to PCA and ICA
    5. 12.5 Prior and likelihood assignments
    6. 12.6 Source modeling
    7. 12.7 Estimation schemes
    8. 12.8 Source separation applications
    9. 12.9 Source characterization
    10. 12.10 Conclusion
    11. References
  20. Chapter 13. Non-negative mixtures
    1. 13.1 Introduction
    2. 13.2 Non-negative matrix factorization
    3. 13.3 Extensions and modifications of NMF
    4. 13.4 Further non-negative algorithms
    5. 13.5 Applications
    6. 13.6 Conclusions
    7. Acknowledgements
    8. References
  21. Chapter 14. Nonlinear mixtures
    1. 14.1 Introduction
    2. 14.2 Nonlinear ICA in the general case
    3. 14.3 ICA for constrained nonlinear mixtures
    4. 14.4 Priors on sources
    5. 14.5 Independence criteria
    6. 14.6 A Bayesian approach for general mixtures
    7. 14.7 Other methods and algorithms
    8. 14.8 A few applications
    9. 14.9 Conclusion
    10. Acknowledgments
    11. Software
    12. References
  22. Chapter 15. Semi-blind methods for communications
    1. 15.1 Introduction
    2. 15.2 Training-based and blind equalization
    3. 15.3 Overcoming the limitations of blind methods
    4. 15.4 Mathematical formulation
    5. 15.5 Channel equalization criteria
    6. 15.6 Algebraic equalizers
    7. 15.7 Iterative equalizers
    8. 15.8 Performance analysis
    9. 15.9 Semi-blind channel estimation
    10. 15.10 Summary, conclusions and outlook
    11. References
  23. Chapter 16. Overview of source separation applications
    1. 16.1 Introduction
    2. 16.2 How to solve an actual source separation problem
    3. 16.3 Overfitting and robustness
    4. 16.4 Illustration with electromagnetic transmission systems
    5. 16.5 Example: Analysis of Mars hyperspectral images
    6. 16.6 Mono- vs multi-dimensional sources and mixtures
    7. 16.7 Using physical mixture models or not
    8. 16.8 Some conclusions and available tools
    9. References
  24. Chapter 17. Application to telecommunications
    1. 17.1 Introduction
    2. 17.2 Data model, statistics and problem formulation
    3. 17.3 Possible methods
    4. 17.4 Ultimate separators of instantaneous mixtures
    5. 17.5 Blind separators of instantaneous mixtures
    6. 17.6 Instantaneous approach versus convolutive approach: simulation results
    7. 17.7 Conclusion
    8. Acknowledgment
    9. References
  25. Chapter 18. Biomedical applications
    1. 18.1 Introduction
    2. 18.2 One decade of ICA-based biomedical data processing
    3. 18.3 Numerical complexity of ICA algorithms
    4. 18.4 Performance analysis for biomedical signals
    5. 18.5 Conclusion
    6. References
  26. Chapter 19. Audio applications
    1. 19.1 Audio mixtures and separation objectives
    2. 19.2 Usable properties of audio sources
    3. 19.3 Audio applications of convolutive ICA
    4. 19.4 Audio applications of SCA
    5. 19.5 Conclusion
    6. Acknowledgments
    7. References
  27. Glossary
  28. Subject Index

Product Information

  • Title: Handbook of Blind Source Separation
  • Author(s): Pierre Comon, Christian Jutten
  • Release date: February 2010
  • Publisher(s): Elsevier Science
  • ISBN: 9780080884943