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Table of contents
1 Introduction
2 From brain signals to functional connectivity and graph analysis
2.1 How to estimate brain connectivity from time series
2.2 Graph representation of brain connectivity networks
2.3 The Graph Signal Processing Framework
2.4 Representation of Time-Varying Networked Data
3 Graph connectivity estimation to detect mental states
3.1 Introduction
3.2 Material and methods
3.2.1 Experimental protocol and preprocessing
3.2.2 Functional connectivity and brain network features
3.2.3 Statistical Analysis and Classification
3.3 Results
3.3.1 EEG network connectivity changes during motor imagery
3.3.2 Modulation of amplitude and phase synchronization between brain signals
3.3.3 Mental state detection in single individuals
3.4 Discussion
3.4.1 Methodological considerations
3.5 Conclusions
4 Improving graph connectivity estimation with graph signal processing
4.1 Introduction
4.2 Related Work
4.3 Signal Model
4.4 Graph Connectivity Denoising
4.5 Jensen divergence of connectivity states
4.5.1 J-Divergence based Laplacian coefficients scoring
4.6 Results on synthetic data
4.6.1 Signal on Graph generation and connectivity estimation
4.6.2 Subspace robustness on synthetic data
4.6.3 J-divergence computation on synthetic data
4.7 Real BCI measurements
4.7.1 Experimental Protocol and Preprocessing
4.7.2 J-divergence of brain connectivity states
4.7.3 Scoring of Laplacian coefficients in beta band
4.7.4 Short-time estimation of Laplacian coefficients in b band
4.8 Conclusion and further work
5 Framework for short-time graph connectivity estimation
5.1 Introduction
5.2 Deep L1-PCA computational framework
5.3 Application to graph synthetic data
5.3.1 Connectivity matrices simulation
5.3.2 Robustness analysis via MSE
5.3.3 Classification framework
5.4 Results on real BCI data
5.4.1 Experimental Protocol and Preprocessing
5.4.2 Functional connectivity estimation procedure
5.4.3 Classification analysis on real EEG data
5.5 Deep L1-PCA applicability in BCI systems
5.6 Conclusions
6 Conclusions and future perspectives
