Unraveling superimposed EEG rhythms with multi-dimensional decomposition.

Scalp-recorded EEG activity reflects a number of oscillatory phenomena, many of which are generated by coupled brain sources or behave as travelling waves. Decomposition of EEG oscillations into sets of coherent processes may help investigation of the underlying functional brain networks. Traditional decomposition methods, such as ICA and PCA, cannot satisfactorily characterize coherent EEG oscillations. Moreover, these methods impose non-physiological constraints (orthogonality, maximal time independence) on the solutions. We introduce the C(3)R-MDD method, that is based on recursive multi-dimensional decomposition (R-MDD). The method allows separation of ongoing EEG into a predefined number of coherent oscillatory processes. Applied to a multichannel complex cross-correlation array (C(3)), the method extracts oscillatory processes characterized by a dominant frequency, spatial amplitude-phase distribution, and stability in time. Introduction of an additional dimension of experimental conditions allows characterization of condition-related dynamics of the processes. In this study, we first used C(3)R-MDD to decompose a simulated signal created by superposition of components with known properties. Meaningful solutions were obtained even with a suboptimal number of components in the model. Second, we applied the method to decompose rhythmic processes in ongoing low- and high-frequency EEG records of two subjects and demonstrated good reproducibility of the components obtained with different solutions, two halves of the EEG record, and different experimental sessions. The C(3)R-MDD method is compared with other types of signal decomposition: real-numbers ICA and real-numbers MDD.