International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 10 Issue: 05 | May 2023
p-ISSN: 2395-0072
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Analysis of EEG Signal using nonextensive statistics Pragati Patel, Ramesh Naidu Annavarapu Department of Physics, School of Physical, Chemical, and Applied Sciences, Pondicherry University, Puducherry, 605014, ---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - Electroencephalogram (EEG) signal is the most effective, quick, and abundant source of information in understanding the brain related phenomenon. New avenues for EEG-based research in non-medical streams can also be seen with the growing number of qualitative and affordable wearable EEG headsets. But it is extremely hard to assess the information from EEG signal. However, information-theoretical approaches have appeared as a potentially beneficial means to gauge variations in the EEG datasets. This article discusses one such approach: the ‘measure of Tsallis entropy (TsEn)’ to explore and investigate the available natural data. This study set out to critically review the renowned research papers on Tsallis entropy-based EEG signal processing to understand the trends in EEG signal processing research. It attempts to provide practitioners and researchers with insights and future directions for applicability of Tsallis entropy for EEG signal processing and with an emphasis on the suitability of EEG research for clinical studies. It reviews about 35 published papers dividing into medical and non-medical domains and discusses the crucial role of Tsallis parameter ‘q’ in studying complex EEG systems. The result shows Tsallis's non-extensive initiatives seem to be more discriminatory than its Shannon counterpart and all other entropy variants and hence, can preferably be used to study the brain. The paper also concludes that Tsallis entropy offers a comprehensive test of any theory and it proves the efficacy of EEG research in clinical detection and therefore is highly significant in biomedical signal processing.
Key Words: Tsallis Statistics, Non-Extensive Entropy, EEG, EEG data-sets, Biomedical Signal Processing. 1.INTRODUCTION In 1803, a mathematician Lazare Carnot developed the entropy theory when he saw that vitality is reduced due to friction and scattering[1, 2]. This entropy concept was mainly used in two branches of physics; statistical mechanics and thermodynamics, in the earlier days of its invention. Later in 1948, this thermodynamic entropy was introduced as data entropy into the world of data analysis by Shannon[3]. Shannon entropy is precisely developed from the Boltzmann-Gibbs (BG) statistical mechanics and standard thermodynamics and was proved to be efficient in the study of the complexity of systems[4, 5]. Despite their colossal effectiveness, this BG concept-led entropy discusses only extensive structures with short-range interactions and fails for nonextensive systems. In 1988, Tsallis proposed an entropic expression with an index q that results in non-extensive statistics. Tsallis entropy, , builds the foundation of non-extensive statistical mechanics. Numerous phenomena have been studied using non-extensive (Tsallis) statistics in a variety of fields, including physics, chemistry, biology, medicine, economics, geophysics, etc. This article focuses on application and significance of Tsallis entropy in EEG data analysis [6][7]. The study of complex structures has drawn significant interest lately, and the brain being the most complex among them. There are various neuroimaging or brain scanning techniques to directly or indirectly image the brain's structure, function, or pharmacology. Owing to its excellent temporal resolution, electroencephalography (EEG) seems to be the most advisable method for studying the temporal variation of brain activity[8]. The brain's electrical activity characterized by EEG is indeed very complicated. Retrieving the right characteristics from this time series is crucial in brain-related research. There is a range of linear and non-linear approaches available to study EEG time series[9]. However, information-theoretical techniques, precisely the nonextensive entropy-based method, recently appeared as a most promising approach for retrieving reliable information from EEG. Tsallis entropy being the most effective and robust information theoretic technique, can lay the foundation for a real-time decision-making aid in many fields, considering its arithmetic coding is quick[10–12]. Tsallis entropy has proven useful in characterizing systems with long-range interactions in the past thirty years[13–20]. This study attempts to review this nonextensive entropy's applicability to EEG analysis for different purposes.
1.1 Tsallis entropy in Biomedical Signal Processing Often, biomedical signals are disruptive and inconsistent. They generate databases that are high-dimensional and complicated. The outcomes of conventional biomedical data analysis techniques may be affected by the existing interference or intrusion in the data. Considering this problem, nonextensive information entropy has emerged as a reliable estimator of complexity or uncertainty in the signal with various implementation scope. Bock et al. have formulated an early detection strategy for
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