Nörogörüntülemede tensör analizi

Acquisition of large amounts of data in neuroimaging research requires development of new methods that can disentangle the underlying information and reveal the features related to cognitive processes. This thesis attempts to propose new methods that favor the multimodality and multidimensionality of the brain data. The main difficulty for the fusion of imaging modalities is the discrepancies in their spatial and temporal resolutions as well as the different physiological processes they reflect. This problem is addressed by decomposing the EEG and fMRI data cast as tensors on both common and discriminant subspaces and computing the common spatial profile from the data on the cortical surface. The Granger causality analysis of brain connectivity is reformulated on tensor space enabling incorporation of tools developed in that area of research. The first approach on this analysis facilitated tensor methods for sparse representation of the connectivity patterns whereas the second method resolved them as atomic structures. General theory and computationally efficient algorithms are presented. The techniques are illustrated on the simultaneous EEG/fMRI recordings for the fusion model and on the fast fMRI data for the connectivity analysis. The proposed approaches may have a wide application area ranging from the early diagnosis of neurological diseases to the brain-computer interface studies.