Parametric spectral modelling of electroencephalography(EEG)

Abstract

Electroencephalograph (EEG) has become an indispensable tool in clinical neurophysiology and related fields. The EEG mainly contains frequency related activities such as alpha, beta, theta, and delta rhythms, which are wide sense stationary, along with non stationary spike and wave discharges and transients. Further, stationary EEG segments are typically preceded and followed by non stationary transitions. The main objective of EEG signal analysis is to extract valid information from the EEG record and present it in a convenient form to the neurologist to enable proper diagnosis. Many analytical techniques have been used for this purpose, and with the advent of fast Fourier transform (FFT) algorithms and minicomputers, spectral analysis techniques have become popular. In the last decade, parametric representation of EEG has gained importance for data reduction, which is significant since practical EEG recordings generate a large amount of data (e.g., 30 minute sessions per subject). In addition to data reduction, parametric representations provide effective computer based classification of EEGs through pattern recognition techniques. Furthermore, parametric methods (unlike non parametric counterparts) can be easily extended to non stationary signals and are indirectly useful for transient detection. These advantages have motivated the development of improved parametric techniques applicable to signals in general and to EEG in particular. Several techniques used in allied fields are also being evaluated for EEG analysis. With these considerations, parametric spectral modeling of EEG has been chosen as the main objective of this thesis. Clinical aspects and classification of EEG are not within the scope of this work. The following topics are covered in the thesis: ________________________________________ I. Pole-Zero Spectral Modeling of EEG Signals Two pole-zero spectral modeling methods-homomorphic prediction and pole-zero modeling by pole-zero decomposition-were considered. Both are based on a combination of linear prediction and homomorphic filtering. These methods were applied to simulated and real EEG signals. Results were compared with Burg’s maximum entropy all pole modeling. Findings show: • Linear prediction-based pole-zero modeling without prior homomorphic filtering gives erroneous spectral estimates. • The proposed methods give accurate spectral fits to the log magnitude spectrum of EEG signals. • Real EEG signals cannot generally be assumed minimum phase, and linear prediction pole-zero modeling provides accurate results only when applied to the minimum phase equivalent of the EEG rather than to EEG directly. ________________________________________ II. Sequential Adaptive Spectral Estimation Using Least Mean Fourth (LMF) Algorithm The LMF adaptive algorithm proposed by Walach and Widrow (1984), which provides lower convergence error than the LMS algorithm for the same convergence speed, was considered for adaptive spectral estimation. The LMF adaptation was extended to the lattice structure, which has advantages over tapped delay line (TDL) structures, including faster convergence and better stability. Observations: • The original LMF algorithm outperforms LMS only when noise is non Gaussian (e.g., uniform, sine, square noise). • LMF requires explicit estimation of noise power, which is impractical in real signals due to inseparability of signal and noise. • To overcome limitations and enable LMF to work with Gaussian noise, the algorithm was modified by: o Converting Gaussian noise into non Gaussian noise by adding square noise. o Adjusting convergence criteria to account for changes in input noise power. With these modifications: • LMF algorithms can be applied to wide sense stationary signals with sufficiently high SNR. • Application of the new LMF TDL and LMF lattice algorithms to noisy sinusoids, simulated EEG, and real EEG showed: o Lower convergence error than their LMS counterparts. o Better resolution. o Superior spectral fit to Burg’s block data spectrum compared to LMS TDL and LMS lattice. ________________________________________ III. Non Stationary Signal Analysis Using the LMF Adaptive Algorithm The modified LMF algorithms were extended to non stationary signals. Because signal power changes with variations in center frequency, bandwidth, and gain over time, the injected square noise must be scaled to maintain the desired SNR. A scaling factor was derived by computing instantaneous signal and noise powers and comparing the instantaneous SNR with the desired SNR. Additionally, injected noise power computation was improved using exponential weighting over a time window. With these modifications, LMF TDL and LMF lattice algorithms were successfully applied to simulated stochastic signals and real EEG. ________________________________________ IV. Application of LMS Predictive Filtering for Muscle Noise Cancellation EEG analysis, like other signal analyses, is affected by noise-primarily extracerebral disturbances such as muscle noise and ECG contamination. Among various artifacts, muscle noise is frequent and often has magnitude many times that of EEG. A hybrid noise reduction approach was used: 1. Low pass filtering to remove noise outside the EEG frequency band. 2. LMS adaptive predictive filtering to remove in band muscle noise. The performance of this filtering approach was studied on simulated and real EEG signals. The effect of muscle noise on parametric EEG representation and the improvement achieved through filtering were also evaluated. A software based EEG simulation method using digital filters was developed to assess system performance