Sparse Wave Packets Discriminate Motor Tasks in EEG-based BCIs

We propose a novel non-linear source separation technique for single-channel, multi-trial Electroencephalogram (EEG). First, a generative model is posited as the generating process behind bandpassed traces. In particular, the inputs are conceived as the state variable of a switching mechanism that samples temporal snippets from two distributions corresponding to a background component and a phasic event or wave packet counterpart. In order to non-linearly separate the sources, we propose a neurophysiologically principled, non- linear mapping to a space of ℓ₂-norms via the Embedding Transform. In this way, the estimated phasic event component - an ideal time series where neuromodulations are emphasized - is isolated for further processing. The algorithm is tested on the Brain-Computer Interface (BCI) Competition 4 dataset 2a. The results not only surpass classic power-based measures, but also highlight the discriminative nature of scale-specific wave packets in motor imagery tasks. The inherent switching mechanism that generates the traces suggests a transient, temporally sparse feature of the neuromodulations that can be further exploited in applications where compression is advantageous.