Signal processing algorithms for minimization of artefacts in electroencephalogram

Abstract

Electroencephalogram (EEG) is a record of the electrical activity of the human brain picked up by applying electrodes on the scalp. One of the major problems associated with the processing of EEG signals is the presence of artefacts (noise) in the recorded signals, which gives rise to serious difficulties in performing meaningful analysis and interpretation. Hence, minimization of these artefacts from recorded EEG signals forms an important part of computerbased EEG processing. In this thesis, we address the problem of minimizing artefacts from contaminated EEG signals and develop efficient signalprocessing algorithms to solve this. Specifically, we consider the minimization of eyemovement artefacts, muscle artefacts, and 50Hz line interference, which are among the most commonly occurring artefacts in recorded EEG signals. The specific contributions of this thesis are as follows:

1. Adaptive Noise Cancellation (ANC) for EOG Artefact Minimization We explore the use of techniques based on the principle of adaptive noise cancellation (ANC) for solving the EOG minimization problem. The ANC setup requires two input signals (i.e., primary and reference), with the reference input assumed to be correlated with either the desired signal or the undesired signal (but not both) in the primary input. This technique is relevant because the frequency bands of EOG and EEG signals overlap, making conventional methods such as lowpass filtering ineffective. We propose ANC schemes that employ the Recursive Least Squares (RLS) algorithm and the Least Mean Square (LMS) algorithm and evaluate their performance using simulated and recorded signals, with the contaminated EEG as the primary input and EOG signals as the reference input. Results show that one reference EOG channel is sufficient for satisfactory minimization of EOG artefacts, and using two reference channels does not improve performance due to high correlation between the EOG references. Performance is compared using signaltonoise ratio (SNR), linear prediction (LP) spectra, and timedomain plots.

2. Nonlinear Modelling for Artefact Estimation Conventional artefactminimization techniques use linear schemes for estimating artefacts. However, because the propagation of EOG from the eyes to EEG electrode sites may be nonlinear, linear schemes can be suboptimal. We model the recorded EEG as the sum of pure EEG and a nonlinear function of EOG. Three LMSbased ANC schemes are proposed:

Linear estimation model Nonlinear model using sigmoid function Nonlinear model using secondorder Volterra function

Convergence analyses for all three algorithms are presented, with detailed derivation of upper and lower bounds for the stepsize parameter of the sigmoidLMS algorithm. Studies on simulated and recorded signals show:

For small stepsizes: VolterraLMS performs best, sigmoidLMS performs worst. For larger stepsizes: sigmoidLMS outperforms the other two. Usable stepsize range decreases with decreasing SNR, especially for sigmoidLMS.

3. NewtonBased Adaptive Algorithms We propose an ANC scheme using Newton’s method for updating filter parameters to minimize EOG artefacts, exploiting its fast convergence relative to LMS. Two models are used:

Linear model leads to the conventional RLS algorithm Nonlinear model using secondorder Volterra function

Because the nonlinear cost function is a scalarvalued matrix function, we reformulate it into a scalarvalued vector function to apply Newton’s method. The resulting Newton algorithm is unstable due to nearsingularity of the Hessian matrix. Hence, the Hessian is approximated to ensure stability and reduce computational complexity. Performance of:

RLS Exact Newton algorithm Approximate Newton algorithm

is evaluated using SNR, LP spectra, and time plots. Results show that the approximate Newton algorithm performs the best.

4. Neural Network (NN)Based Artefact Minimization We develop EOG artefactminimization schemes based on feedbacktype Neural Networks. The EEG enhancement problem is translated into the NN framework by defining an appropriate energy function from which the neuron model is derived. Three NNbased artefactestimation schemes are proposed:

Linear model Sigmoidbased nonlinear model Volterrabased nonlinear model

Simulation studies using SNR, LP spectra, and timedomain plots reveal that the NN scheme using Volterra nonlinearity is superior.

5. Singular Value Decomposition (SVD) for Artefact Separation We explore the use of singular value decomposition (SVD) for extracting EEG from EOGcontaminated EEG recordings. This is possible because EEG and EOG signals are orthogonal. Studies using simulated and recorded signals (from left/right eye positions and Fp1/Fp2 scalp electrodes) show that SVD is highly effective. Only one EOG recording is required for satisfactory artefact removal.

6. Minimization of OutofBand Noise Outofband noise often contaminates EEG recordings. We propose a linearphase FIR lowpass filter (with finitewordlength precision and designed using a compensation procedure) to minimize such noise. Three filtering configurations are investigated:

Cascading Twicing Sharpening

Twicing and sharpening result in nonlinear phase characteristics; therefore, modifications are proposed to achieve linear phase while improving magnitude characteristics. These filters are applied to:

50Hz powerline artefacts Muscle artefacts

Studies using SNR and time plots show that the modified sharpened filter performs the best. Similar results are observed with recorded signals.

Summary This thesis proposes several signalprocessing algorithms for the minimization of artefacts from EEG signals. It provides a detailed treatment of EOG artefact minimization and also addresses the removal of outofband artefacts such as 50Hz powerline noise and muscle artefacts.