Nonlinear Approach to Brain Signal Modeling

Nonlinear Approach to Brain Signal Modeling

Tugce Balli (University of Essex, UK) and Ramaswamy Palaniappan (University of Essex, UK)
DOI: 10.4018/978-1-60566-026-4.ch453
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Abstract

Biological signal is a common term used for time series measurements that are obtained from biological mechanisms and basically represent some form of energy produced by the biological mechanisms. Examples of such signals are electroencephalogram (EEG), which is the electrical activity of brain recorded by electrodes placed on the scalp; electrocardiogram (ECG), which is electrical activity of heart recorded from chest, and electromyogram (EMG), which is recorded from skin as electrical activity generated by skeletal muscles (Akay, 2000). Nowadays, biological signals such as EEG and ECG are analysed extensively for diagnosing conditions like cardiac arrhythmias in the case of ECG and epilepsy, memory impairments, and sleep disorders in case of EEG. Apart from clinical diagnostic purposes, in recent years there have been many developments for utilising EEG for brain computer interface (BCI) designs (Vaughan & Wolpaw, 2006). The field of signal processing provides many methods for analysis of biological signals. One of the most important steps in biological signal processing is the extraction of features from the signals. The assessment of such information can give further insights to the functioning of the biological system. The selection of proper methods and algorithms for feature extraction (i.e., linear/nonlinear methods) are current challenges in the design and application of real time biological signal analysis systems. Traditionally, linear methods are used for the analysis of biological signals (mostly in analysis of EEG). Although the conventional linear analysis methods simplify the implementation, they can only give an approximation to the underlying properties of the signal when the signal is in fact nonlinear. Because of this, there has been an increasing interest for utilising nonlinear analysis techniques in order to obtain a better characterisation of the biological signals. This chapter will lay the backgrounds to linear and nonlinear modeling of EEG signals, and propose a novel nonlinear model based on exponential autoregressive (EAR) process, which proves to be superior to conventional linear modeling techniques.
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Background Information

EEG Signal Processing

In recent years, the field of biological signal processing has seen an explosive growth. In particular, there have been many research studies on EEG signals for:

  • Diagnosis of certain neurological conditions such as sleep disorders, memory impairments and epilepsy;

  • Extracting relevant features for classification of different mental states;

  • Understanding the dynamics and underlying mechanisms of the brain.

Figure 1 shows the basic steps in the analysis of EEG signals, these are: preprocessing which includes the removal of noises such as the baseline noise, powerline interference and eye blink contamination; feature extraction, which extracts representative values of the signals through modeling techniques, and classification, where the extracted features are classified in specific for the application, such as discrimination between different mental states or neurological conditions. Note that the feature extraction step is not necessarily followed by classification—the features can also be used in understanding the nature and underlying dynamics of the signals, for example in investigating a certain brain disorder. The selection of appropriate feature extraction methods for obtaining a better representation of the EEG signals is the most challenging step in EEG signal processing. This can be approached in two ways namely the linear and nonlinear modeling techniques.

Figure 1.

The basic steps in EEG signal analysis

Key Terms in this Chapter

EAR: Exponential Autoregressive model, a nonlinear extension of Autoregressive model.

Nonlinear Signal: A nonlinear signal is generally defined as the signal generated by the system that does not obey superposition and scaling properties.

Stochastic (Random) Process: Opposite of deterministic processes in which the future states of the system can not be predicted precisely. In other words, even if the initial states of the process are known there are many states that the process can go where some states are more probable than others.

White Noise: A random signal that has equal amount of power at all frequency bands.

Linear Signal: A linear signal is generally defined as the output of a linear shift invariant system that is driven by Gaussian white noise.

Shift-Invariant System: A shift-invariant system is known as a system that input-output relationship does not vary with time such that; let y[n] be the response of the system to input x[n] , for any delay t , the response of the system to input x[n-t] will be y[n-t] .

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