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
Inhaltsverzeichnis
1;Front cover;1 2;Half page;2 3;Title page;4 4;Copyright page;5 5;Contents;6 6;About the editors;20 7;Preface;22 8;Contributors;24 9;Chapter 1. Introduction;26 9.1;1.1. Genesis of blind source separation;26 9.2;1.2. Problem formalization;35 9.3;1.3. Source separation methods;36 9.4;1.4. Spatial whitening, noise reduction and PCA;38 9.5;1.5. Applications;40 9.6;1.6. Content of the handbook;40 9.7;References;44 10;Chapter 2. Information;48 10.1;2.1. Introduction;48 10.2;2.2. Methods based on mutual information;49 10.3;2.3. Methods based on mutual information rate;70 10.4;2.4. Conclusion and perspectives;86 10.5;References;87 11;Chapter 3. Contrasts;90 11.1;3.1. Introduction;90 11.2;3.2. Cumulants;92 11.3;3.3. MISO contrasts;94 11.4;3.4. MIMO contrasts for static mixtures;103 11.5;3.5. MIMO contrasts for dynamic mixtures;117 11.6;3.6. Constructing other contrast criteria;126 11.7;3.7. Conclusion;127 11.8;References;128 12;Chapter 4. Likelihood;132 12.1;4.1. Introduction: Models and likelihood;132 12.2;4.2. Transformation model and equivariance;134 12.3;4.3. Independence;141 12.4;4.4. Identifiability, stability, performance;147 12.5;4.5. Non-Gaussian models;156 12.6;4.6. Gaussian models;161 12.7;4.7. Noisy models;167 12.8;4.8. Conclusion: A general view;173 12.9;4.9. Appendix: Proofs;177 12.10;References;178 13;Chapter 5. Algebraic methods after prewhitening;180 13.1;5.1. Introduction;180 13.2;5.2. Independent component analysis;186 13.3;5.3. Diagonalization in least squares sense;190 13.4;5.4. Simultaneous diagonalization of matrix slices;195 13.5;5.5. Simultaneous diagonalization of third-order tensor slices;199 13.6;5.6. Maximization of the tensor trace;199 13.7;References;200 14;Chapter 6. Iterative algorithms;204 14.1;6.1. Introduction;204 14.2;6.2. Model and goal;205 14.3;6.3. Contrast functions for iterative BSS/ICA;206 14.4;6.4. Iterative search algorithms: Generalities;211 14.5;6.5. Iterative whitening;217 14.6;6.6. Classical adaptive algorithms;218 14.7;6.7. R
elative (natural) gradient techniques;224 14.8;6.8. Adapting the nonlinearities;228 14.9;6.9. Iterative algorithms based on deflation;230 14.10;6.10. The FastICA algorithm;233 14.11;6.11. Iterative algorithms with optimal step size;241 14.12;6.12. Summary, conclusions and outlook;245 14.13;References;246 15;Chapter 7. Second-order methods based on color;252 15.1;7.1. Introduction;252 15.2;7.2. WSS processes;253 15.3;7.3. Problem formulation, identifiability and bounds;257 15.4;7.4. Separation based on joint diagonalization;270 15.5;7.5. Separation based on maximum likelihood;285 15.6;7.6. Additional issues;295 15.7;References;301 16;Chapter 8. Convolutive mixtures;306 16.1;8.1. Introduction and mixture model;306 16.2;8.2. Invertibility of convolutive MIMO mixtures;308 16.3;8.3. Assumptions;312 16.4;8.4. Joint separating methods;317 16.5;8.5. Iterative and deflation methods;326 16.6;8.6. Non-stationary context;334 16.7;References;347 17;Chapter 9. Algebraic identification of under-determined mixtures;350 17.1;9.1. Observation model;350 17.2;9.2. Intrinsic identifiability;351 17.3;9.3. Problem formulation;357 17.4;9.4. Higher-order tensors;362 17.5;9.5. Tensor-based algorithms;370 17.6;9.6. Appendix: expressions of complex cumulants;385 17.7;References;387 18;Chapter 10. Sparse component analysis;392 18.1;10.1. Introduction;392 18.2;10.2. Sparse signal representations;395 18.3;10.3. Joint sparse representation of mixtures;399 18.4;10.4. Estimating the mixing matrix by clustering;413 18.5;10.5. Square mixing matrix: Relative Newton method;421 18.6;10.6. Separation with a known mixing matrix;428 18.7;10.7. Conclusion;435 18.8;10.8. Outlook;437 18.9;References;439 19;Chapter 11. Quadratic time-frequency domain methods;446 19.1;11.1. Introduction;446 19.2;11.2. Problem statement;447 19.3;11.3. Spatial quadratic t - f spectra and representations;452 19.4;11.4. Time-frequency points selection;460 19.5;11.5. Separation algorithms;465 19.6;11.6. Practical and computer simulat
ions;477 19.7;11.7. Summary and conclusion;487 19.8;References;489 20;Chapter 12. Bayesian approaches;492 20.1;12.1. Introduction;492 20.2;12.2. Source separation forward model and notations;493 20.3;12.3. General Bayesian scheme;495 20.4;12.4. Relation to PCA and ICA;496 20.5;12.5. Prior and likelihood assignments;502 20.6;12.6. Source modeling;507 20.7;12.7. Estimation schemes;518 20.8;12.8. Source separation applications;519 20.9;12.9. Source characterization;524 20.10;12.10. Conclusion;533 20.11;References;534 21;Chapter 13. Non-negative mixtures;540 21.1;13.1. Introduction;540 21.2;13.2. Non-negative matrix factorization;540 21.3;13.3. Extensions and modifications of NMF;546 21.4;13.4. Further non-negative algorithms;559 21.5;13.5. Applications;564 21.6;13.6. Conclusions;567 21.7;References;567 22;Chapter 14. Nonlinear mixtures;574 22.1;14.1. Introduction;574 22.2;14.2. Nonlinear ICA in the general case;575 22.3;14.3. ICA for constrained nonlinear mixtures;579 22.4;14.4. Priors on sources;592 22.5;14.5. Independence criteria;595 22.6;14.6. A Bayesian approach for general mixtures;600 22.7;14.7. Other methods and algorithms;605 22.8;14.8. A few applications;606 22.9;14.9. Conclusion;609 22.10;References;611 23;Chapter 15. Semi-blind methods for communications;618 23.1;15.1. Introduction;618 23.2;15.2. Training-based and blind equalization;620 23.3;15.3. Overcoming the limitations of blind methods;622 23.4;15.4. Mathematical formulation;624 23.5;15.5. Channel equalization criteria;626 23.6;15.6. Algebraic equalizers;629 23.7;15.7. Iterative equalizers;635 23.8;15.8. Performance analysis;641 23.9;15.9. Semi-blind channel estimation;653 23.10;15.10. Summary, conclusions and outlook;657 23.11;References;658 24;Chapter 16. Overview of source separation applications;664 24.1;16.1. Introduction;664 24.2;16.2. How to solve an actual source separation problem;667 24.3;16.3. Overfitting and robustness;670 24.4;16.4. Illustration with electromagnetic transmission systems;6
73 24.5;16.5. Example: Analysis of Mars hyperspectral images;683 24.6;16.6. Mono- vs multi-dimensional sources and mixtures;693 24.7;16.7. Using physical mixture models or not;697 24.8;16.8. Some conclusions and available tools;701 24.9;References;702 25;Chapter 17. Application to telecommunications;708 25.1;17.1. Introduction;708 25.2;17.2. Data model, statistics and problem formulation;712 25.3;17.3. Possible methods;721 25.4;17.4. Ultimate separators of instantaneous mixtures;737 25.5;17.5. Blind separators of instantaneous mixtures;741 25.6;17.6. Instantaneous approach versus convolutive approach: simulation results;751 25.7;17.7. Conclusion;754 25.8;References;755 26;Chapter 18. Biomedical applications;762 26.1;18.1. Introduction;762 26.2;18.2. One decade of ICA-based biomedical data processing;764 26.3;18.3. Numerical complexity of ICA algorithms;783 26.4;18.4. Performance analysis for biomedical signals;788 26.5;18.5. Conclusion;797 26.6;References;797 27;Chapter 19. Audio applications;804 27.1;19.1. Audio mixtures and separation objectives;804 27.2;19.2. Usable properties of audio sources;812 27.3;19.3. Audio applications of convolutive ICA;815 27.4;19.4. Audio applications of SCA;831 27.5;19.5. Conclusion;839 27.6;References;840 28;Glossary;846 29;Index;848
