Sparse Wave Packets Discriminate Motor Tasks in EEG-Based BCIs

Abstract

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 $ell_2$--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.