Matrix and tensor decomposition methods for joint blind source separation : theory and application to functional imaging data / von M.Sc. Isabell Lehmann ; Erster Gutachter: Prof. Dr. Peter Schreier, Zweite Gutachterin: Prof. Dr. Tülay Adali. Paderborn, 2025
Inhalt
- Abstract
- Zusammenfassung
- Acknowledgments
- Introduction
- Joint Blind Source Separation
- Notation
- Blind Source Separation for K=1 dataset
- Joint Blind Source Separation for K>1 datasets
- Source identification conditions for BSS and JBSS
- A small note on the use of samples
- Matrix and tensor decomposition methods for BSS and JBSS
- Independent Component Analysis
- Independent Vector Analysis
- Canonical Correlation Analysis
- Multiset Canonical Correlation Analysis
- PARAFAC2
- Connections between JBSS methods
- Connection between all-at-once analytical sumcor and all-at-once analytical maxvar
- Connection between all-at-once analytical sumcor and deflationary analytical maxvar
- Connection between PARAFAC2 and IVA-G
- Summary
- Source identification conditions for BSS and JBSS
- Source identification conditions of ICA for BSS (K=1 dataset)
- Source identification conditions of IVA for JBSS (K ≥2 datasets)
- Source identification conditions of CCA for JBSS (K=2 datasets)
- Source identification conditions of mCCA for JBSS (K≥2 datasets)
- Source identification conditions of mCCA-sumcor
- Source identification conditions of mCCA-maxvar
- Source identification conditions of mCCA-minvar
- Source identification conditions of mCCA-genvar
- Source identification conditions of mCCA-ssqcor
- Simulation study of source identification conditions of mCCA
- Summary
- Appendix: Proof of source identification conditions of sumcor
- Identifying the relationship structure among multiple datasets using JBSS
- Problem formulation
- Proposed method for identifying the relationship structure among multiple datasets
- Step 1: Estimation of SCVs
- Step 2: Identification of common and structured SCVs
- Step 3: Identification of the relationship structure using the structured SCVs
- Computational complexity of the proposed method
- Simulations
- Summary
- JBSS for multi-task fMRI data analysis
- fMRI dataset and preprocessing
- IVA-G and PARAFAC2 for multi-task fMRI data fusion
- Identifying the relationship structure among multi-task fMRI datasets
- Summary
- Deriving 3D functional brain networks from multi-slice fUS data using JBSS
- Conclusion
- List of publications
- Acronyms
- List of symbols
- List of figures
- List of tables
- Bibliography