| Brain-Computer Interface (BCI) systems aim to provide a non-muscular channel for the brain to control external devices using electrical activities of the brain. These BCI systems can be used in various applications, such as controlling a wheelchair, neuroprosthesis, or speech synthesizer for disabled individuals, navigation in virtual environment, and assisting healthy individuals in performing highly demanding tasks. Motor-imagery BCI systems in particular are based on decoding imagination of motor tasks, e.g., to control the movement of a wheelchair or a mouse curser on the computer screen and move it to the right or left directions by imagining right/left hand movement. During the past decade, there has been a growing interest in utilization of electroencephalogram (EEG) signals for non-invasive motor-imagery BCI systems, due to their low cost, ease of use, and widespread availability.;During motor-imagery tasks, multichannel EEG signals exhibit task-specific features in both spatial domain and spectral (or frequency) domain. This thesis studies the statistical characteristics of the multichannel EEG signals in these two domains and proposes a new approach for spatio-spectral feature extraction in motor-imagery BCI systems. This approach is based on the fact that due to the multichannel structure of the EEG data, its spatio-spectral features have a matrix-variate structure. This structure, which has been overlooked in the literate, can be exploited to design more efficient feature extraction methods for motor-imagery BCIs.;Towards this end, this research work adopts a matrix-variate Gaussian model for the spatio-spectral features, which assumes a separable Kronecker product structure for the covariance of these features. This separable structure, together with the general properties of the Gaussian model, enables us to design new feature extraction schemes which can operate on the data in its inherent matrix-variate structure to reduce the computational cost of the BCI system while improving its performance. Throughout this thesis, the proposed matrix-variate model and its implications will be studied in various different feature extraction scenarios. |
