Tensor-based preprocessing of combined EEG/MEG data

Due to their good temporal resolution, electroencephalography (EEG) and magnetoencephalography (MEG) are two often used techniques for brain source analysis. In order to improve the results of source localisation algorithms applied to EEG or MEG data, tensor-based preprocessing techniques can be used to separate the sources and reduce the noise. These methods are based on the Canonical Polyadic (CP) decomposition (also called Parafac) of space-time-frequency (STF) or space-time-wave-vector (STWV) data. In this paper, we analyse the combination of EEG and MEG data to enhance the performance of the tensor-based preprocessing. To this end, we consider the joint CP decomposition of two (or more) third order tensors with one or two identical loading matrices. We present the necessary modifications for several classical CP decomposition algorithms and examine the gain on performance in the EEG/MEG context by means of simulations.