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Complex Detection Using the Continuous Wavelet Transform ARS Medica Tomitana - 2018; 4(24): pag. 144 - 152 doi: 10.2478/arsm-2018-0031 K - COMPLEX DETECTION USING THE CONTINUOUS WAVELET TRANSFORM Dumitrescu Cătălin1, Copaci Carmen2, Iliescu Dan3, Hangan Tony3, Ionescu Ana-Maria3, Bobe Alexandru4 1 Department of Artificial Intelligence, University Politehnica of Bucharest, Romania 2 UTI Grup SA 3 Faculty of Medicine, “Ovidius” University, Constanţa, Romania 4 Faculty of Mathematics and Informatics, “Ovidius” University, Constanţa, Romania Dan Iliescu Faculty of Medicine, Univeristy „Ovidius” of Constanta, Universitatii Alee No. 1, Campus B, Constanta, Romania email: [email protected] phone: +40 722973928 ABSTRACT The wide variety of waveform in EEG signals and the high non-stationary nature of many of them is one of the main difficulties to develop automatic detection system for them. In sleep stage classification a relevant transient wave is the K-complex. This paper comprehend the developing of two algorithms in order to achieve an automatic K-complex detection from EEG raw data. These algorithms are based on a time-frequency analysis and two time-frequency techniques, the Short Time Fourier Transform (STFT) and the Continuous Wavelet Transform (CWT), are tested in order to find out which one is the best for our purpose, being of two wavelet functions to measure the capability of them to detect K-complex and to choose one to be employed in the algorithms. The first algorithm is based on the energy distribution of the CWT detecting the spectral component of the K-complex. The second algorithm is focused on the morphology of the K-complex / sleep spindle waveform after the CWT. Evaluating the algorithms results reveals that a false K-complex detection is as important as real K-complex detection. Keywords: EEG, K-complex, Short Time Fourier Transform, Continous Wavelet Transform, wave morphology Introduction signals, and inferring different sleep stages from the detection of these waveforms. However, Since the discovery of the the strong non-stationarity nature (transient Electroencephalogram (EEG) by the German phenomena) of EEG signals has represented psychiatrist Hans Berger in 1924 extensive one of the main difficulties in the developing of studies about electrical activity of the human reliable systems for sleep classification. brain have been carried out. One of these A non-stationary signal is defined as a studies correspond to sleep stage classification. short time event whose frequency content vary In the last twenty years several researches and in time. A traditional analysis technique, for this significance advances have been made in the field kind of signals, that provide an image of the of automatic sleep stage classification since it is frequency contents of a signal as a function of one of the diagnostic tools needed for assessment the time is the time-frequency analysis. Several of a number of sleep disorders. Automatic sleep methods or time-frequency distributions can be analysis is based on the detection of various used, for example the spectrogram (Short Time waveforms in the EEG and other bioelectric Fourier Transform) which calculate the power 144 spectrum of the investigated signal seen through to implement a time-frequency analysis the a time windows function that slide along the time Continuous Wavelet Transform will be employed axis. In this work we will concentrated in another because it has been probe to be an efficient tool time-frequency distribution, the Continuous in extraction of transient characteristics from a Wavelet Transform (CWT). The CWT can collection of raw data. Therefore, the problem be seen as an operator that takes a signal and statement of this work is to build and evaluate produces a function depending of two variables: a K-complex detection system using the wavelet time and scale. In this way the CWT is able to transform and, posteriorly, evaluate the algorithm provide information of features corresponding to performance trying to find out possible important the signal that are dependent on the scale used. faults that may affect the system. The scale-dependent structure is strongly linked with the frequency content of the signal giving Relevant Theory to the CWT a great potential for detecting and identifying signals with exotic spectral features This chapter will try to cover all the like transients behavior. necessary theoretical background in order to Detection of transient signals in give the reader a better approach to the sleep Electroencephalograms has been a subject of stage classification and time-frequency analysis research for several years. In sleep EEG one of the using wavelet transform. It begins with the most relevant transient signals is the K-complex. basic concepts of sleep classification and a brief In literature we have found a sort of methods description of the bioelectrical signal involved, and algorithms for detection of K-complexes particularly the electroencephalogram (EEG). using Neural Networks, feature based approach, Then, an explanation of the relevant EEG independent component analysis, adaptive filters, waveforms is given. As a first step toward a statistics methods among others. In order to process of EEG transient signal detection, the introduce the reader in the K-complex detection Joint Time – Frequency Analysis are explained. field, we will give a brief explanation about some Finally, a review of the definition and basic studies which have been carried out in this field. proprieties of the Continuous Wavelet Transform, In this report we will try to probe whether with the corresponding example and reason or no using wavelet transform we can improve of why this Transform will be used for time- detection of K-complexes. At the beginning frequency analysis are given. of the last century the Haar transform gave 1.1 Sleep Analysis the first step in the wavelet career, but this Sleep analysis is a medical tool of vital transform was not very used until early eighties, importance for the diagnosis and treatment of when geophysicians, theorical physicians and several kinds of sleep disturbance and psychiatric mathematicians developed a solid theory for or neurological disorders. Today, a typical study Wavelet. Since then, Wavelet has been used in of sleep includes records of the muscle tone several applications, like signal processing, (EMG), of the eye movements (EOG) and of the data compress, time-frequency analysis, cerebral activity (EEG) although depending on the multirresolution analysis, statistics, vibrations clinical purpose other physiological parameters and many others. like respiration, heart rate, blood pressure, body In the last fifteen years wavelet has temperature, hormonal secretions are used. On been widely used in EEG analysis as much as the basis of such recordings a certain number epilepsy and Alzheimer diagnosis as sleep stage of sleep stage are distinguished by criteria that classification. have been standardized by general by general The main of this work is to extract agreement (1). information from sleep EEG raw data about 1.2 Electroencephalogram (EEG) the presence of K-complexes. We decided to The physiological exploration of sleep work in the time-frequency domain instead involves the study of several signals, such as of either pure time domain or pure frequency electroencephalogram (EEG), electro-ocular domain as previous works in this field. In order (EOG), electromyogram (EMG), blood oxygen 145 measurement, temperature and electrocardiogram emerge theta and secondary transient sleeping (ECG). The recording of these signals is called a spindles with 14 Hz frequency, 40 to 50 μV polysomnogram. amplitude and no more than one K complex An electroencephalogram represents the with the frequency of 33 Hz, amplitude of 100 activity of bioelectric signals that is determined by μV. In a healthy person they must be present the electrical activity of the brain. The oscillations simultaneously in both the left and right of the brain are called brainwaves. They have hemispheres. Furthermore, the wave magnitude certain characteristics including: amplitude increases significantly in the central brain areas. ranging between 10-500 μV and frequency ●Stage 3: indicates slow (stable) sleep, between 0.5-40 Hz. For the measurement of brain high amplitude slow waves called delta waves waves one uses the international standardized (delta rhythm - 75μV), appear on 20-50% of system called “International Federation 10-20 samples, theta waves become irregular. At this system”. stage, transient waves such as sleep spindles and The result of a polysomnogram is visualized complex K still persist by using a hypnogram which distinguishes sleep ●Stage 4: indicates the rapid (paradoxical) stages by analyzing successive sequences of 30 sleep state, delta wave increases occur in more seconds of sleep. than 50% of samples (delta-75μV), theta waves These stages are defined by the nature of appear regularly, and the secondary waves the signals encountered in the EEG, including disappear. Paradoxical sleep or REM (Rapid Eye the delta, theta, alpha or beta waves, which are Movement) gives the impression of a superficial identified by their frequency domains. sleep, although the depth of sleep is deeper than The main wave types are: in the other stages of sleep (muscle relaxation and Alpha Research has shown that in a person rapid eye movements. It is a sleeping phase with who is awake, the presence of alpha waves dreams, with secretions of growth hormones, indicates her/his relaxation. Alpha waves range having a
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