Christian Jutten, PhD, is Emeritus Professor of signal processing at University Grenoble Alpes and Honorary Senior Member at the Institut Universitaire de France. He is globally recognized for his pioneering research contributions to blind source separation, and has published widely on this and related subjects. Leonardo Tomazeli Duarte, PhD, is Associate Professor at the School of Applied Sciences, University of Campinas (Unicamp), Brazil. He has researched extensively into blind source separation and other aspects of signal processing and data science methods. Saïd Moussaoui, PhD, is a Researcher and Professor in Signal and Image Processing at École Centrale de Nantes, France. He has published widely on signal processing, source separation, image restoration and other related subjects.

• About the Editors xiiiList of Contributors xvForeword xviiPreface xxiNotation xxiii1 Overview of Source Separation 1Christian Jutten, Leonardo Tomazeli Duarte, and Saïd Moussaoui1.1 Introduction 11.2 The Problem of Source Separation 31.3 Statistical Methods for Source Separation 151.4 Source Separation Problems in Physical--Chemical Sensing 241.5 Source Separation Methods for Chemical--Physical Sensing 301.6 Organization of the Book 352 Optimization 43Emilie Chouzenoux and Jean-Christophe Pesquet2.1 Introduction to Optimization Problems 432.2 Majorization--Minimization Approaches 502.3 Primal-Dual Methods 722.4 Application to NMR Signal Restoration 832.5 Conclusion 913 Non-negative Matrix Factorization 103David Brie, Nicolas Gillis, and Saïd Moussaoui3.1 Introduction 1033.2 Geometrical Interpretation of NMF and the Non-negative Rank 1053.3 Uniqueness and Admissible Solutions of NMF 1123.4 Non-negative Matrix Factorization Algorithms 1183.5 Applications of NMF in Chemical Sensing. Two Examples of Reducing Admissible Solutions 1293.6 Conclusions 1414 Bayesian Source Separation 151Saïd Moussaoui, Leonardo Tomazeli Duarte, Nicolas Dobigeon, and Christian Jutten4.1 Introduction 1514.2 Overview of Bayesian Source Separation 1524.3 Statistical Models for the Separation in the Linear Mixing 1594.4 Statistical Models and Separation Algorithms for Nonlinear Mixtures 1734.5 Some Practical Issues on Algorithm Implementation 1774.6 Applications to Case Studies in Chemical Sensing 1824.7 Conclusion 1915 Geometrical Methods -- Illustration with Hyperspectral Unmixing 201José M. Bioucas-Dias and Wing-Kin Ma5.1 Introduction 2015.2 Hyperspectral Sensing 2025.3 Hyperspectral Mixing Models 2065.4 Linear HU Problem Formulation 2085.5 Dictionary-Based Semiblind HU 2225.6 Minimum Volume Simplex Estimation 2275.7 Applications 2395.8 Conclusions 2446 Tensor Decompositions: Principles and Application to Food Sciences 255Jérémy Cohen, Rasmus Bro, and Pierre Comon6.1 Introduction 2556.2 Tensor Decompositions 2616.3 Constraints in Decompositions 2736.4 Coupled Decompositions 2796.5 Algorithms 2866.6 Applications 297References 307Index 325

Christian Jutten, PhD, is Emeritus Professor of signal processing at University Grenoble Alpes and Honorary Senior Member at the Institut Universitaire de France. He is globally recognized for his pioneering research contributions to blind source separation, and has published widely on this and related subjects. Leonardo Tomazeli Duarte, PhD, is Associate Professor at the School of Applied Sciences, University of Campinas (Unicamp), Brazil. He has researched extensively into blind source separation and other aspects of signal processing and data science methods. Saïd Moussaoui, PhD, is a Researcher and Professor in Signal and Image Processing at École Centrale de Nantes, France. He has published widely on signal processing, source separation, image restoration and other related subjects.

• About the Editors xiiiList of Contributors xvForeword xviiPreface xxiNotation xxiii1 Overview of Source Separation 1Christian Jutten, Leonardo Tomazeli Duarte, and Saïd Moussaoui1.1 Introduction 11.2 The Problem of Source Separation 31.3 Statistical Methods for Source Separation 151.4 Source Separation Problems in Physical--Chemical Sensing 241.5 Source Separation Methods for Chemical--Physical Sensing 301.6 Organization of the Book 352 Optimization 43Emilie Chouzenoux and Jean-Christophe Pesquet2.1 Introduction to Optimization Problems 432.2 Majorization--Minimization Approaches 502.3 Primal-Dual Methods 722.4 Application to NMR Signal Restoration 832.5 Conclusion 913 Non-negative Matrix Factorization 103David Brie, Nicolas Gillis, and Saïd Moussaoui3.1 Introduction 1033.2 Geometrical Interpretation of NMF and the Non-negative Rank 1053.3 Uniqueness and Admissible Solutions of NMF 1123.4 Non-negative Matrix Factorization Algorithms 1183.5 Applications of NMF in Chemical Sensing. Two Examples of Reducing Admissible Solutions 1293.6 Conclusions 1414 Bayesian Source Separation 151Saïd Moussaoui, Leonardo Tomazeli Duarte, Nicolas Dobigeon, and Christian Jutten4.1 Introduction 1514.2 Overview of Bayesian Source Separation 1524.3 Statistical Models for the Separation in the Linear Mixing 1594.4 Statistical Models and Separation Algorithms for Nonlinear Mixtures 1734.5 Some Practical Issues on Algorithm Implementation 1774.6 Applications to Case Studies in Chemical Sensing 1824.7 Conclusion 1915 Geometrical Methods -- Illustration with Hyperspectral Unmixing 201José M. Bioucas-Dias and Wing-Kin Ma5.1 Introduction 2015.2 Hyperspectral Sensing 2025.3 Hyperspectral Mixing Models 2065.4 Linear HU Problem Formulation 2085.5 Dictionary-Based Semiblind HU 2225.6 Minimum Volume Simplex Estimation 2275.7 Applications 2395.8 Conclusions 2446 Tensor Decompositions: Principles and Application to Food Sciences 255Jérémy Cohen, Rasmus Bro, and Pierre Comon6.1 Introduction 2556.2 Tensor Decompositions 2616.3 Constraints in Decompositions 2736.4 Coupled Decompositions 2796.5 Algorithms 2866.6 Applications 297References 307Index 325

Christian Jutten, PhD, is Emeritus Professor of signal processing at University Grenoble Alpes and Honorary Senior Member at the Institut Universitaire de France. He is globally recognized for his pioneering research contributions to blind source separation, and has published widely on this and related subjects. Leonardo Tomazeli Duarte, PhD, is Associate Professor at the School of Applied Sciences, University of Campinas (Unicamp), Brazil. He has researched extensively into blind source separation and other aspects of signal processing and data science methods. Saïd Moussaoui, PhD, is a Researcher and Professor in Signal and Image Processing at École Centrale de Nantes, France. He has published widely on signal processing, source separation, image restoration and other related subjects.

• About the Editors xiiiList of Contributors xvForeword xviiPreface xxiNotation xxiii1 Overview of Source Separation 1Christian Jutten, Leonardo Tomazeli Duarte, and Saïd Moussaoui1.1 Introduction 11.2 The Problem of Source Separation 31.3 Statistical Methods for Source Separation 151.4 Source Separation Problems in Physical--Chemical Sensing 241.5 Source Separation Methods for Chemical--Physical Sensing 301.6 Organization of the Book 352 Optimization 43Emilie Chouzenoux and Jean-Christophe Pesquet2.1 Introduction to Optimization Problems 432.2 Majorization--Minimization Approaches 502.3 Primal-Dual Methods 722.4 Application to NMR Signal Restoration 832.5 Conclusion 913 Non-negative Matrix Factorization 103David Brie, Nicolas Gillis, and Saïd Moussaoui3.1 Introduction 1033.2 Geometrical Interpretation of NMF and the Non-negative Rank 1053.3 Uniqueness and Admissible Solutions of NMF 1123.4 Non-negative Matrix Factorization Algorithms 1183.5 Applications of NMF in Chemical Sensing. Two Examples of Reducing Admissible Solutions 1293.6 Conclusions 1414 Bayesian Source Separation 151Saïd Moussaoui, Leonardo Tomazeli Duarte, Nicolas Dobigeon, and Christian Jutten4.1 Introduction 1514.2 Overview of Bayesian Source Separation 1524.3 Statistical Models for the Separation in the Linear Mixing 1594.4 Statistical Models and Separation Algorithms for Nonlinear Mixtures 1734.5 Some Practical Issues on Algorithm Implementation 1774.6 Applications to Case Studies in Chemical Sensing 1824.7 Conclusion 1915 Geometrical Methods -- Illustration with Hyperspectral Unmixing 201José M. Bioucas-Dias and Wing-Kin Ma5.1 Introduction 2015.2 Hyperspectral Sensing 2025.3 Hyperspectral Mixing Models 2065.4 Linear HU Problem Formulation 2085.5 Dictionary-Based Semiblind HU 2225.6 Minimum Volume Simplex Estimation 2275.7 Applications 2395.8 Conclusions 2446 Tensor Decompositions: Principles and Application to Food Sciences 255Jérémy Cohen, Rasmus Bro, and Pierre Comon6.1 Introduction 2556.2 Tensor Decompositions 2616.3 Constraints in Decompositions 2736.4 Coupled Decompositions 2796.5 Algorithms 2866.6 Applications 297References 307Index 325