Coupled CP Decomposition of EEG and MEG Magnetometer and Gradiometer Measurements via the Coupled SECSI Framework

Recent research has shown that the joint processing of simultaneously recorded EEG-MEG signals can be beneficial compared to the separate analysis of data if the corresponding tensors have one of their factor matrices in common. In this study, we perform a joint CP decomposition of simultaneously recorded EEG and MEG magnetometer as well as gradiometer measurements via a new extension of the coupled SEmi-Algebraic framework for the approximate CP decomposition via SImultaneous matrix diagonalization (SECSI) to jointly factorize several tensors with at least one factor matrix in common. In case of the biomedical data, the four measured tensors have the factor matrix in the frequency domain in common. The developed coupled SECSI algorithm allows extracting the signal sources even in ill-conditioned scenarios. In the final processing step, coupled SECSI chooses the best out of a variety of possible factor matrix estimates, i.e., a combination that leads to the smallest value of the reconstruction error. However, for data tensors that do not exhibit significant coupling, the uncoupled solution can also be selected. The results are evaluated on measured as well as on synthetic data and compared with other state-of-the-art approaches.