Analysis of Event-Related Potentials Elicited During Information Processing Tasks

This work is motivated by the problem of estimation and classification of different electroencephalography (EEG) patterns elicited during various information processing tasks. Since the discovery of Hans Berger in 1929, interest in developing algorithms to process human brain and mind information by analyzing the EEG and ERP signals has been constantly growing. Both the EEG and ERP signals have been shown to be related to many psychological processes involved in attention, memory and motor control. Moreover, both types of signals have been proven to be useful in classification of different mental and cognitive tasks. Consequently, the idea of developing a brain computer interface (BCI), i.e. to use the brain electrical signals in order to control remote devices, has emerged. Research in this field has faced various engineering and physiological problems. These include, among others, low signal-to-noise ratio (SNR), overlapping spectra between the ERP and the spontaneous EEG, high intrasubjects and intersubjects variability, signals characterized by nonstationarity and nonergodicity and unknown number and location of intracranial sources and unknown intrabrain wave propagation channels. Therefore, it is required to employ appropriate methods for estimating and classifying these signals. In this work, novel methods for single-trial EEG estimation and classification are developed. First, a model-based approach for multichannel EEG classification is introduced. The approach is based on parallel hidden Markov models (PHMMs) and a maximum-likelihoodbased decision rule. The performances of the PHMM classifier are studied using an artificial EEG database and two real databases. The results show that the PHMM algorithm outperforms other existing methods, with an improvement of 2% and 10%, in the classification rates for the two real databases, respectively, comparing to the best reported method. One of the main obstacles in EEG estimation is the presence of modeling mismatch. In order to cope with this problem, a new estimator is derived based on the minimum meansquare error (MMSE) criterion with constraints on the firstand second-order statistics of the parameters of interest. The constrained MMSE (CMMSE) estimator provides a suboptimal solution, which guarantees that the firstand second-order statistical properties of the estimated signal match those of the parameter of interest. The CMMSE estimator is found to be robust to signal distribution mismatch, since it incorporates statistical information on the parameters of interest and restricts the solution space accordingly. The performance of the CMMSE estimator under different mismatch conditions is studied both analytically and via simulations using several examples. It is shown that with no distribution mismatch, the CMMSE performance is slightly lower than the optimal MMSE, while in the presence of signal distribution mismatch, the CMMSE estimator outperforms the MMSE estimator and several other commonly used estimators. The CMMSE estimator preserves the firstand second-order statistics of the parameter of interest, while higher order statistics might not match to the true statistics. Hence, the idea of the constrained estimator is further extended to an estimator which incorporates constraints on the probability density function (PDF) of the parameter of interest. The statistical constraints are based on Gaussian mixture model (GMM) representation of the PDF. This estimator guarantees that the statistical properties of the estimated signal match those of the parameter of interest. Since a closed form expression for this estimator is difficult to obtain, an approximated estimator, termed as GMM-CMMSE, which is based on a weighted sum of linear CMMSE estimators, is proposed. The performance of the GMM-CMMSE estimator under different mismatch conditions is studied via simulations using several examples. It is shown that with no distribution mismatch, the GMM-CMMSE performance is slightly lower than the optimal MMSE. However, in the presence of signal distribution mismatch, the GMMCMMSE estimator is superior to the MMSE estimator, and the other tested estimators. In addition, the GMM-CMMSE is easy to implement, since it can be represented by a weighted sum of linear CMMSE estimators. The CMMSE and GMM-CMMSE estimators are employed for single-trial EEG estimation. Some simulation experiments are performed using real EEG signals acquired from seven subjects while performing five mental tasks. The performance of the CMMSE and the GMMCMMSE estimators are compared with those of an ICA-based estimator and the Wiener filter. It is shown that the CMMSE and the GMM-CMMSE estimators outperform both the ICAbased estimator and the Wiener filter in most of the illustrated SNRs. Further evaluation of the estimators performances using real databases of various types of response-related EEGs, and the impact of the proposed estimators on the classification rates, is dependent upon acquiring or obtaining an appropriate database, and is therefore a topic for future research. In addition, it is postulated that incorporation of mutual information between different data channels and/or incorporation of inter-channel statistical constraints may improve the performances of the CMMSE and GMM-CMMSE estimators. Beyond the use of the above-mentioned estimators for EEG processing, they may be utilized in many other signal processing applications in which the MMSE estimator is employed, such as Kalman filter, expectation-maximization algorithm, etc. Therefore, these estimators are of great importance in signal processing theory and applications. Hence, the main contributions of this dissertation are the development of a novel multichannel classification algorithm based on parallel HMMs, the development of robust constrained estimators, and the implementation of these estimators for single-trial EEG estimation.