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Table of contents
1 Motivations and organisation
1.1 Motivations
1.2 Thesis organisation
2 Introduction on hyperspectral imaging
2.1 Hyperspectral imaging concept
2.1.1 Hyperspectral sensors
2.1.2 Hyperspectral reflectance data
2.2 Spectral mixing models
2.2.1 Linear mixing model
2.2.2 Nonlinear mixing models
2.3 Spectral unmixing
2.3.1 Linear unmixing
2.3.2 Nonlinear unmixing
2.4 Incorporating spatial information into unmixing
3 Blind & fully constrained linear unmixing
3.1 Introduction
3.2 Group lasso, unit sum, and positivity (GLUP)
3.2.1 Optimization problem
3.2.2 ADMM algorithm
3.3 Reduced noise GLUP (NGLUP)
3.3.1 Optimization problem
3.3.2 ADMM algorithm
3.4 Experimental results
3.4.1 Synthetic Data
3.4.2 Real data: Cuprite
3.5 Conclusion
4 Graph-based regularized linear unmixing
4.1 Introduction
4.2 Image to graph mapping
4.2.1 Defining the edge set
4.2.2 Defining the weights
4.2.3 Graph operators
4.3 Graph based regularization
4.3.1 Quadratic Laplacian regularization
4.3.2 Nonlocal TV regularization
4.4 ADMM algorithm
4.4.1 Quadratic Laplacian regularization
4.4.2 Nonlocal TV regularization
4.5 A note on complexity
4.6 Experiments
4.6.1 Experiments with the Quadratic Laplacian regularization
4.6.2 Experiments with nonlocal TV regularization
4.7 Conclusion
5 Supervised nonlinear unmixing with vector-valued kernel functions
5.1 Introduction
5.2 Nonlinear mixing model
5.2.1 Model Description
5.2.2 RKHS of vector-valued functions
5.2.3 Kernel design
5.3 Estimation algorithm
5.3.1 Optimization problem
5.3.2 Iterative algorithm
5.3.3 Implementation details
5.4 Experiments
5.4.1 Synthetic data
5.4.2 Real data: Gulf of Lion
5.5 Conclusion
6 Spatial regularization for nonlinear unmixing
6.1 Introduction
6.2 Vector-valued formulation
6.3 Kernel design and regularization
6.4 Estimation algorithm
6.5 Experiments on synthetic data
6.5.1 Illustrative example
6.5.2 Spatial data set
6.6 Conclusion
7 Concluding remarks
7.1 Summary of objectives and contributions
7.2 Future research directions
