Resolving Spectral Mixtures, Volume 30

• Preface
• Foreword
• Chapter 1: Introduction
  • Abstract
  • 1 Introduction
  • 2 The Spectral Mixture Problem
  • 3 Book Content and Organization
• Chapter 2: Multivariate Curve Resolution-Alternating Least Squares for Spectroscopic Data
  • Abstract
  • 1 MCR: The Concept and the Link with Spectroscopic Data
  • 2 MCR-ALS: Algorithm and Data Set Configuration
  • 3 MCR-ALS Applied to Process Analysis
  • 4 MCR-ALS Applied to HSI Analysis
  • 5 MCR-ALS and Quantitative Analysis
  • 6 MCR-ALS and Other Bilinear Decomposition Methods
• Chapter 3: Spectral Unmixing Using the Concept of Pure Variables
  • Abstract
  • 1 Introduction
  • 2 Case Studies
  • 3 Spectral Unmixing with Pure Variables
  • 4 Chasing the Pure Variables
  • 5 Investigation of Purity Characteristics
  • 6 Other Ways to Find the Pure Variables
  • 7 Pure Variables and MCR-ALS
  • 8 Discussion and Conclusions
• Chapter 4: Ambiguities in Multivariate Curve Resolution
  • Abstract
  • 1 Multivariate Curve Resolution and Ambiguities
  • 2 Evaluation of MCR Ambiguities
  • 3 Estimation of the Extension of Rotation Ambiguities and of Their MCR Feasible Solutions
  • 4 MCR Constraints and Their Implementation
  • 5 Implementation of the MCR-BANDS Method
  • 6 Example of Calculation of MCR Feasible Solutions Using the MCR-BANDS Method
  • 7 Comparison of Solutions Obtained by Different MCR Methods
  • 8 Comparison of the Ranges of MCR Feasible Solutions Obtained by Different Methods
  • 9 Conclusions
• Chapter 5: On the Analysis and Computation of the Area of Feasible Solutions for Two-, Three-, and Four-Component Systems
  • Abstract
  • 1 Introduction
  • 2 MCR Methods
  • 3 The Area of Feasible Solutions
  • 4 The AFS for Two-Component Systems
  • 5 Feasibility of Points in the AFS
  • 6 AFS Computations for Three-Component Systems
  • 7 AFS Computations for Four-Component Systems
  • 8 Reduction of the Rotational Ambiguity by Soft Constraints Represented in the AFS
  • 9 Geometric Shapes of the AFS and AFS Dynamics
  • 10 The FACPACK Toolbox for AFS Computations
  • 11 Outlook and Open Problems
• Chapter 6: Linear and Nonlinear Unmixing in Hyperspectral Imaging
  • Abstract
  • 1 Spectral Mixture Analysis
  • 2 Linear Unmixing
  • 3 Nonlinear Unmixing
  • 4 Experiments: Unmixing EELS Data
  • 5 Conclusion
  • Acknowledgments
• Chapter 7: Independent Components Analysis: Theory and Applications
  • Abstract
  • 1 Introduction
  • 2 Theory
  • 3 Some Applications of ICA
  • 4 Conclusion
• Chapter 8: Bayesian Positive Source Separation for Spectral Mixture Analysis
  • Abstract
  • 1 Introduction
  • 2 Geometrical Interpretation of the NMF Model
  • 3 The Bayesian Positive Source Separation Algorithm
  • 4 Applications
  • 5 Conclusion
• Chapter 9: Multivariate Curve Resolution of Wavelet Compressed Data
  • Abstract
  • 1 Introduction
  • 2 Theory
  • 3 Experimental Details
  • 4 Discussion of Results
  • 5 Conclusion
  • Acknowledgments
• Chapter 10: Chemometric Resolution of Complex Higher Order Chromatographic Data with Spectral Detection
  • Abstract
  • 1 Introduction
  • 2 Instrument Design and Utilization to Produce High-Order Chemical Separations Data
  • 3 Chemometric Resolution Methods
  • 4 Applications and Conclusions
• Chapter 11: Multivariate Curve Resolution of (Ultra)Fast Photoinduced Process Spectroscopy Data
  • Abstract
  • 1 Introduction
  • 2 Photoinduced Processes
  • 3 Time-Resolved Spectroscopy
  • 4 MCR of TRS Data
  • 5 Applications
  • 6 Concluding Remarks
• Chapter 12: Experimental and Data Analytical Approaches to Automating Multivariate Curve Resolution in the Analysis of Hyperspectral Images
  • Abstract
  • 1 Introduction
  • 2 Theory of MCR Analyses
  • 3 Approaches to Improve the Probability of Successful MCR Solutions
  • 4 Comparison of Standard and Automated Preprocessing Approaches to MCR Analyses of Realistically Simulated and Real Hyperspectral Confocal Fluorescence Images
  • 5 Conclusions
  • Acknowledgments
• Chapter 13: Multiresolution Analysis and Chemometrics for Pattern Enhancement and Resolution in Spectral Signals and Images
  • Abstract
  • 1 Introduction
  • 2 Methods
  • 3 Applications
  • 4 Remarks
  • Acknowledgments
• Chapter 14: A Smoothness Constraint in Multivariate Curve Resolution-Alternating Least Squares of Spectroscopy Data
  • Abstract
  • 1 Introduction
  • 2 Smoothing Signals and Images
  • 3 Smoothness Constraints in MCR-ALS
  • 4 Case Studies
  • 5 Concluding Remarks
  • Acknowledgments
• Chapter 15: Super-Resolution in Vibrational Spectroscopy: From Multiple Low-Resolution Images to High-Resolution Images
  • Abstract
  • 1 Introduction
  • 2 The Super-Resolution Concept
  • 3 Criteria to Measure the Spatial Resolution in Imaging Spectroscopy
  • 4 Case Study #1: Super-Resolution Concept in MIR Spectroscopy [16]
  • 5 Optimization and Study of the Super-Resolution Concept in Near-Infrared Spectroscopy [19]
  • 6 Optimization and Study of the Super-Resolution Concept for Raman Confocal Imaging [24]
  • 7 Conclusion
• Chapter 16: Multivariate Curve Resolution for Magnetic Resonance Image Analysis: Applications in Prostate Cancer Biomarkers Development
  • Abstract
  • 1 Introduction
  • 2 State-of-the-Art Methods
  • 3 New Biomarkers Development
  • 4 Conclusions
  • Acknowledgments
• Chapter 17: Endmember Library Approaches to Resolve Spectral Mixing Problems in Remotely Sensed Data: Potential, Challenges, and Applications
  • Abstract
  • 1 Introduction
  • 2 Endmember Library-Based SMA Approaches
  • 3 Challenges of Endmember Library-Based SMA Approaches
  • 4 Applications of Endmember Library Approaches to Resolve Spectral Mixing Problems in Remotely Sensed Data
  • 5 Conclusions
  • Acknowledgments
• Chapter 18: Spectral–Spatial Unmixing Approaches in Hyperspectral VNIR/SWIR Imaging
  • Abstract
  • 1 Introduction
  • 2 Background on Linear Spectral Unmixing
  • 3 Use of Spatial Information in Unmixing Process
  • 4 Conclusions
• Chapter 19: Sparse-Based Modeling of Hyperspectral Data
  • Abstract
  • 1 Introduction
  • 2 Theory: Sparse Methods
  • 3 Sparse-Based Image Exploration: Applications
  • 4 Conclusions
• Index

Resolving Spectral Mixtures: With Applications from Ultrafast Time-Resolved Spectroscopy to Superresolution Imaging offers a comprehensive look into the most important models and frameworks essential to resolving the spectral unmixing problem—from multivariate curve resolution and multi-way analysis to Bayesian positive source separation and nonlinear unmixing. Unravelling total spectral data into the contributions from individual unknown components with limited prior information is a complex problem that has attracted continuous interest for almost four decades.

Spectral unmixing is a topic of interest in statistics, chemometrics, signal processing, and image analysis. For decades, researchers from these fields were often unaware of the work in other disciplines due to their different scientific and technical backgrounds and interest in different objects or samples. This led to the development of quite different approaches to solving the same problem. This multi-authored book will bridge the gap between disciplines with contributions from a number of well-known and strongly active chemometric and signal processing research groups.

Among chemists, multivariate curve resolution methods are preferred to extract information about the nature, amount, and location in time (process) and space (imaging and microscopy) of chemical constituents in complex samples. In signal processing, assumptions are usually around statistical independence of the extracted components. However, the chapters include the complexity of the spectral data to be unmixed as well as dimensionality and size of the data sets. Advanced spectroscopy is the key thread linking the different chapters. Applications cover a large part of the electromagnetic spectrum. Time-resolution ranges from femtosecond to second in process spectroscopy and spatial resolution covers the submicronic to macroscopic scale in hyperspectral imaging.

• Demonstrates how and why data analysis, signal processing, and chemometrics are essential to the spectral unmixing problem
• Guides the reader through the fundamentals and details of the different methods
• Presents extensive plots, graphical representations, and illustrations to help readers understand the features of different techniques and to interpret results
• Bridges the gap between disciplines with contributions from a number of well-known and highly active chemometric and signal processing research groups

Analytical and bioanalytical chemists, spectroscopists, chemometricians, and scientists working in signal processing, image processing, food & drugs, and pharmaceuticals