Using the multi-linear rank-(Lr, Lr, 1) decomposition for the detection of the 200 Hz band activity in somatosensory evoked magnetic fields and somatosensory evoked electrical potentials

Abstract

Studies of oscillations in the frequency band between 80 Hz and 250 Hz for EEG (Electroencephalogram) and MEG (Magnetoencephalogram) have achieved fruitful results of detecting and interpreting both normal and pathological activities in the brain. This contribution presents a new description of the 200 Hz band activity in somatosensory evoked electrical potentials (SEPs) and somatosensory evoked magnetic fields (SEFs) with the help of tensor decompositions. The SEPs and SEFs elicited by electrical stimulation of the median nerve were measured in eight healthy volunteers. A time-frequency analysis of the SEPs and SEFs produced the time-dependent spectra of the signals that were arranged into three-dimensional EEG and MEG data tensors, respectively. We then propose a novel multi-way component analysis approach by employing a tensor decomposition known as the multi-linear rank-( $L_{r}$ , $L_{r}$ , 1) decomposition. Featuring the ability to extract channel-dependent spectral signatures, this method is able to separate the 200 Hz band activity-related signal components in SEPs and SEFs. Via a coupled version of the multi-linear rank-( $L_{r}$ , $L_{r}$ , 1) decomposition, a joint processing of these simultaneous EEG and MEG recordings has been achieved. The advantages of the joint processing over the separate processing of EEG or MEG alone have been both qualitatively and quantitatively validated in seven out of eight subjects