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.