Source Separation in Physical-Chemical Sensing

About the Editors xiii

List of Contributors xv

Foreword xvii

Preface xxi

Notation xxiii

1 Overview of Source Separation 1
Christian Jutten, Leonardo Tomazeli Duarte, and Saïd Moussaoui

1.1 Introduction 1

1.2 The Problem of Source Separation 3

1.3 Statistical Methods for Source Separation 15

1.4 Source Separation Problems in Physical--Chemical Sensing 24

1.5 Source Separation Methods for Chemical--Physical Sensing 30

1.6 Organization of the Book 35

2 Optimization 43
Emilie Chouzenoux and Jean-Christophe Pesquet

2.1 Introduction to Optimization Problems 43

2.2 Majorization--Minimization Approaches 50

2.3 Primal-Dual Methods 72

2.4 Application to NMR Signal Restoration 83

2.5 Conclusion 91

3 Non-negative Matrix Factorization 103
David Brie, Nicolas Gillis, and Saïd Moussaoui

3.1 Introduction 103

3.2 Geometrical Interpretation of NMF and the Non-negative Rank 105

3.3 Uniqueness and Admissible Solutions of NMF 112

3.4 Non-negative Matrix Factorization Algorithms 118

3.5 Applications of NMF in Chemical Sensing. Two Examples of Reducing Admissible Solutions 129

3.6 Conclusions 141

4 Bayesian Source Separation 151
Saïd Moussaoui, Leonardo Tomazeli Duarte, Nicolas Dobigeon, and Christian Jutten

4.1 Introduction 151

4.2 Overview of Bayesian Source Separation 152

4.3 Statistical Models for the Separation in the Linear Mixing 159

4.4 Statistical Models and Separation Algorithms for Nonlinear Mixtures 173

4.5 Some Practical Issues on Algorithm Implementation 177

4.6 Applications to Case Studies in Chemical Sensing 182

4.7 Conclusion 191

5 Geometrical Methods -- Illustration with Hyperspectral Unmixing 201
Jose M. Bioucas-Dias and Wing-Kin Ma

5.1 Introduction 201

5.2 Hyperspectral Sensing 202

5.3 Hyperspectral Mixing Models 206

5.4 Linear HU Problem Formulation 208

5.5 Dictionary-Based Semiblind HU 222

5.6 Minimum Volume Simplex Estimation 227

5.7 Applications 239

5.8 Conclusions 244

6 Tensor Decompositions: Principles and Application to Food Sciences 255
Jeremy Cohen, Rasmus Bro, and Pierre Comon

6.1 Introduction 255

6.2 Tensor Decompositions 261

6.3 Constraints in Decompositions 273

6.4 Coupled Decompositions 279

6.5 Algorithms 286

6.6 Applications 297

References 307

Index 325