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The human brain is unquestionably the most complex organ of the body as it controls and processes its movement and senses. A healthy brain is able to generate responses to the signals it receives, and transmit messages to the body. Some neural disorders can impair the communication between the brain and the body preventing the transmission of these messages. Brain Computer Interfaces (BCIs) are devices that hold immense potential to assist patients with such disorders by analyzing brain signals, translating and classifying various brain responses, and relaying them to external devices and potentially back to the body. Classifying motor imagery brain signals where the signals are obtained based on imagined movement of the limbs is a major, yet very challenging, step in developing Brain Computer Interfaces (BCIs). Of primary importance is to use less data and computationally efficient algorithms to support real-time BCI. To this end, in this thesis we explore and develop algorithms that exploit the sparse characteristics of EEGs to classify these signals. Different feature vectors are extracted from EEG trials recorded by electrodes placed on the scalp. In this thesis, features from a small spatial region are approximated by a sparse linear combination of few atoms from a multi-class dictionary constructed from the features of the EEG training signals for each class. This is used to classify the signals based on the pattern of their sparse representation using a minimum-residual decision rule. We first attempt to use all the available electrodes to verify the effectiveness of the proposed methods. To support real time BCI, the electrodes are reduced to those near the sensorimotor cortex which are believed to be crucial for motor preparation and imagination. In a second approach, we try to incorporate the effect of spatial correlation across the neighboring electrodes near the sensorimotor cortex. To this end, instead of considering one feature vector at a time, we use a collection of feature vectors simultaneously to find the joint sparse representation of these vectors. Although we were not able to see much improvement with respect to the first approach, we envision that such improvements could be achieved using more refined models that can be subject of future works. The performance of the proposed approaches is evaluated using different features, including wavelet coefficients, energy of the signals in different frequency sub-bands, and also entropy of the signals. The results obtained from real data demonstrate that the combination of energy and entropy features enable efficient classification of motor imagery EEG trials related to hand and foot movements. This underscores the relevance of the energies and their distribution in different frequency sub-bands for classifying movement-specific EEG patterns in agreement with the existence of different levels within the alpha band. The proposed approach is also shown to outperform the state-of-the-art algorithm that uses feature vectors obtained from energies of multiple spatial projections. |
