HILBERT-HUANG TRANSFORM USED FOR EEG SIGNAL ANALYSIS

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1 The 6 th edition of the Interdisciplinarity in Engineering International Conference Petru Maior University of Tîrgu Mureş, Romania, 2012 HILBERT-HUANG TRANSFORM USED FOR EEG SIGNAL ANALYSIS Lajos LOSONCZI # *1, László BAKÓ #2, Sándor-Tihamér BRASSAI #3 and László-Ferenc MÁRTON #4 * Lambda Communication Ltd. Tirgu Mures, Str. Avram Iancu Nr. 37, Romania 1 lajos@lambda.ro # NSRG - Neural Systems Research Group, Sapientia University Tirgu-Mures/Corunca, Şoseaua Sighişoarei 1C, Romania 2 lbako@ms.sapientia.ro 3 tiha@ms.sapientia.ro 4 martonlf@ms.sapientia.ro ABSTRACT The EEG signals are recorded between electrodes placed in standard positions on the scalp. They have a typical amplitude of µv and a frequency spectrum from Hz. The potential at the scalp derives from electrical activity of large synchronized groups of neurons inside the brain. EEG activity in particular frequency bands is often correlated with particular cognitive states. There are many ways to approach the understanding of brainwaves but the analysis of electroencephalograms (EEG) continues to be a problem due to our limited understanding of the signal origin. It is hard to design an effective evaluation method for the recorded signals. The Hilbert-Huang Transform (HHT) is in the centre of this study. This procedure is giving a deep insight of timefrequency structure of time series. The HHT method is exemplified on EEG signals recorded by our NSRG-team. In this paper we emphasize the technical aspects of the procedure and not the biological significance of the results. Keywords: Hilbert-Huang transform, Instantaneous frequency (ifr), Instantaneous phase (iph), intrinsic mode function (IMF) 1. Introduction The EEG is thus like a symphony, which is a complex mixture of sounds, changing in time and in space. Most EEG signals (waveforms) originate in the brain s outer layer (the cerebral cortex), believed responsible for many individual thoughts, emotions and behaviors. To the mathematical or theoretical considerations, many of these waveforms appear typical of nonlinear and non-stationary systems. This is a very important observation. It is reasonable to assume EEG signals as the summed effects of locally generated activity in small networks and more globally generated activity involving spatially extensive networks (up to the global scale of the entire cerebral cortex). The brain is a massively parallel processor each processor contains many thousands of cell systems. A cell system is an organized assembly of networks of different cell types. The preponderance of one or more rhythms at one time and the combination of task specific frequencies (combination in time and in space) is peculiar for the activities, of the brain. The analyses of the observed brainwave frequencies, analyzing the EEG data on a segment-by-segment basis, can approximate us to understand how information processing in neural systems are performed. The analysis of brain waves plays an important role also in clinical diagnosis. Despite the impressive advancements, interpreting brain waves remains quite difficult. Brain data are often complex and overwhelming. Techniques for nonlinear and nonstationary signal processing may play an increasingly important role in the area of brain research. We have recorded EEG signals using a twoelectrodes (Ag / AgCl + gel), reference electrodes mounted on specific cortical areas on scalp, and an eleven-electrode array (semi dry, salted water) placed over the left and right cortical regions (sensorimotor, 361

2 motor, frontal, occipital). We have used programmable sampling frequencies (128Hz, 256Hz). The recording electrodes are placed over the scalp, respecting the International System conventions. The recording device was not for clinical use. The off-line signal processing was performed on a PC. The used signal recordings have been performed on the members of NSRG research group without any previous teaching periods. It is important to understand that the brain does not communicate, or do its processing, using the EEG. It is something a secondary measure, as the temperature of an electronic circuit, or such as the vibration of an engine. It is known that EEG reflects correlated synaptic activity of cortical assembly of neurons. Specifically, the scalp electrical potentials that produce EEG are generally thought to be caused by the extracellular summation of ionic currents caused by electrical activity of individual cells from a synchronized assembly. EEG's can detect changes over milliseconds. Rhythmic activity is characterizing the normal frequency structure of the recorded waveforms and is divided into bands by frequency. The rhythmic activity within a certain frequency range was noted to have a certain distribution over the scalp or a certain biological significance. The proposed HHT is giving a detailed inside of this frequency ranges. For a deeper understanding of WT, at first, we must consider the biologically explainable frequency contain of EEG signals. 1. Delta component is considered a signal in 0 to 4 Hz band. Usually the lower band of 0.3 to 1.5Hz is specific of deep sleep Brain State (BS), namely the slow wave sleep (SWS) but has been found in some continuous attention tasks related signals. This component is specific for frontal lobe of adult persons (F in 10/20 standard), but posteriorly can be recorded at children. These components have high amplitude. 2. Theta component is considered a signal in 4 to 8 Hz band. It is related to exploratory tasks but sometimes to drowsiness (paradoxical sleep) or idle or meditative state of a person. 3. Alpha component is considered a signal in 8 to 13 Hz band (in sensorimotor cortex shows the rest of motor neurons called Mu component). It is characteristic mainly to posterior regions of head, both side but with higher amplitude on non-dominant hemisphere. It is specific for closing the eyes, reflecting (relaxed) state or with inhibition control in different locations across the brain. In clinical recording, it is a sign of coma state. 4. Beta component is considered a signal in 13 to 30 Hz band. This component has symmetrical distribution on both side of the brain. It is a low amplitude wave. It is characteristic to anxious thinking or active state in alert (working) behavior. Beta activity is closely linked to motor behavior and is generally attenuated during active movements 5. Gamma component is considered a signal in 30 to 110 Hz band. It is mainly characteristic to sensorimotor cortex. It shows cross-modal sensory processing (related to the combination of two different perceptions). It is shown during short term memory matching of recognition (objects, sounds, tactile sensations). It must be mentioned, that the frequency borders of the presented bands is not strict (specific boundaries depending on the range they choose to focus on), overlapping can be considered and sometimes the band type name is different in different studies. 2. Methods Traditional data-analysis methods are all based on linear and stationary assumptions. The Hilbert Huang transform (HHT) is an empirically based dataanalysis method. Its basis of expansion is adaptive, so that it can produce physically meaningful representations of data from nonlinear and nonstationary processes. The universally accepted mathematical paradigm of data expansion in terms of an a priori established basis would need to be modified. The convolution computation of the a priori basis creates more problems than solutions. A necessary condition to represent nonlinear and non-stationary data is to have an adaptive basis. An a priori defined function cannot be relied on as a basis, no matter how sophisticated the basis function might be. For non-stationary and nonlinear data, where adaptation is absolutely necessary other than a Hilbert-Huang transform is not usable. Most of the studies rely on the temporal and/or spectral features of the pre-processed EEG signals. Usually the spatial as well as temporal and spectral information have been considered by means of multivariate autoregressive (MVAR) modeling of the multi-channel EEG [1]. In [2] is a presentation of an algorithm based on a method of HHT for automatic location of alpha and theta waves in electroencephalogram. New method in seizure classification based on HHT is in [3]. One example of clinical use of HHT is relative to Alcoholic EEG research [4]. Electroencephalographic measures indicate an overall slowing subsequent to meditation, with theta and alpha activation related to proficiency of practice. For these studies a HHT method is presented in [5]. There are several studies and publications related to engineering (control engineering based on Brain Computer Interface - BCI) processes based on basic HHT methods. The HHT consists of two parts: empirical mode decomposition (EMD) and Hilbert spectral analysis (HSA). This method is potentially viable for nonlinear and non-stationary data analysis, especially for time-frequency-energy representations. The 362

3 physically meaningful way to describe such a system is in terms of the instantaneous frequency, which will reveal the intra-wave frequency modulations. The easiest way to compute the instantaneous frequency is by using the Hilbert transform. Hilbert transform is a convolution of a time series and a 1 t category function. Using the Hilbert transform of a time series, it is possible to define an analytic signal, in which the Hilbert transform constitute the imaginary part. Each complex expression can provide, in polar representation, its amplitude and a phase. The result of Hilbert transform of a time series is an analytical time series, a complex valued signal. Its amplitude and phase is time dependent. For this reason it was introduced three new concepts, the instantaneous amplitude and the instantaneous phase functions. The time derivative of phase function is called instantaneous frequency function. Even with the Hilbert transform, defining the instantaneous frequency still involves considerable controversy. It should lead to the problem of having frequency values being equally likely to be positive and negative for any given time series (positive or negative energy). As a result, the past applications of the Hilbert transform are all limited to the narrow band-passed signals, which have with the same number of extreme values and zero-crossings. But filtering is a linear operation, altering its harmonics and creating a distortion of the waveform. To avoid this situation, before Hilbert transform it is necessary to use the so called empirical mode decomposition (EMD) introduced by N. Huang in This is intuitive, direct, and adaptive method, with an a posteriori-defined basis from the decomposition method, based on and derived directly from the data. The basic idea of EMD is that each time series consists of different simple intrinsic modes of oscillations. Each intrinsic mode, linear or nonlinear, represents a simple oscillation, which will have the same number of extreme values and zero-crossings and the oscillation will also be symmetric with respect to the local mean. These functions are the mono-components or the intrinsic mode functions (IMF). It is known from literature that IMFs must have two basic properties: The number of extreme values and the number of zero-crossings must be the same or differ at most by one, At any point (time moment) the mean value of signal lower and higher envelope is zero. Any IMFs are simple, general oscillatory events as the harmonic function components modulated in amplitude and phase. There are several EMD methods developed after the first Huang procedure. Each of them is, usually, very time consuming repetitive algorithm [6], [7], [8]. 3. Results At first, there is a test signal created to bring out the HHT method efficiency in signal analysis. We are starting with the test signal: y = sin( 2π 5 t) + sin(2π 10 t + π /3) (1) Figure 1 is the representation of this test signal (red). The following figures have been created using MATLAB codes developed by NSRG group and based on knowledge accumulated in different domain of signal processing. This is a detailed use of the method for oscillations of biological source, one of the first attempts of this kind. π π + π Fig. 1 The used test signal (red) and its components: y = sin( 2 5 t) + sin(2 10 t / 3) 363

4 As it was mentioned before, the Hilbert-Huang transform is a combination of two basic procedures. We have a signal. If that signal is of biological origin, then we must consider it as having nonlinear, nonstationary signal characteristics. We know that for such kind of signals, the Fourier transform is not usable, or it is usable with the risk to lose the expected accuracy of the analysis. The HHT is avoiding some of Fourier s method inaccuracy. The first part of HHT is the so called EMD (Empirical Mode Decomposition). It is a time consuming method for long recordings with a high sampling frequency rate. For our test signal, the EMD is about to detect the peaks and troughs of the original signal, calculate a mean signal value and using the original algorithm of Huang [8], the IMF components are calculated. The number of these mono-components (IMF) is not known from the beginning. An IMF is a special phase, frequency and amplitude modulated signal. In case of an IMF, we can use the Hilbert transform, not resulting a negative energy subspace in timefrequency transform. The result of the Hilbert transform is an analytic (complex structure) function with its corresponding amplitude and a phase function components. The derivative of phase function is called the instantaneous frequency component. For our test signal, two mono-components have been found. One has 5Hz, the other 10Hz, as we expected. The following two figures are about these two IMFs (Fig. 2 and Fig. 3). In these figures, on the top subplot, there are visible not a straight line for the instantaneous frequency components (there must be a single, constant frequency component there), as we expect from a theoretical point of view, but here, there is an oscillatory state. This is because of the reduced (and finite) sampling rate of the generated test signal. It is also visible a short deformation of the mono-component at the beginning and of the signal. This is an effect of the short length of it. Fig. 2 - The IMF and its structure in IMF1, as it results in HHT from the test signal The middle subplots are the IMFs, in Fig. 2 the IMF1 and in Fig. 3 the IMF2. In an ideal case, both are pure harmonic functions. In a real case, these are close to an ideal harmonics. The bottom subplot in both figures shows the phase function of the IMFs. The domain of values are in [-π, +π], interval and each period is covering a trough to trough interval. If an event is considered at a time moment, from the instantaneous phase function, it is easy to find out the phase value relative the oscillatory state. 364

5 Fig. 3 - The IMF and its structure in IMF2, as it results in HHT from the test signal We have used the HHT method for EEG signals. The EEG signals have been recorded by members of NSRG group with a non-clinical equipment, Emotive Epoc product, with 14 electrodes in 10/20 standard and 256Hz sampling rate. The examined EEG signals are shown on Fig. 4. Fig EEG recording with EmotiveEpoc recording system. The channel s signals are event related potentials, repeated at every 10 seconds in an one minute interval. The channel s name are using 10/20 EEG standards. 365

6 Fig. 5 - The F8 Channel signal, (from fig. 4). The blue is the original signal, the red is the added IMFs without IMF1, IMF2, IMF3. This is not a filtering method. The result is better, then using a low pass classical filter, because a filter is a system with its all inconvenient characteristics (phase distortion, amplitude modulation at cutting frequency). Fig. 6 - The first eight IMF component of the F8 channel signal (see Fig. 5) 366

7 To understand much better what is resulting from a mono-component, in the following figures we will detail two of them, showing their instantaneous frequency function (ifr) and also the instantaneous phase function (iph). It is important to understand, in case of nonlinear and non-stationary signals the notions as Period and Phase are reduced to ifr and iph. It is hard interpret these notions in a classical way of thinking. For EEG type of signals, all the history of events are incorporated in a long sequence of moments described by the ifr and iph. Each moment has its separate significance. It depends also on the used sampling frequency of the signal. As an example, a theta oscillation is not a harmonic function but it is a sequence of instantaneous theta events with different frequency and phase and amplitude in each moment. Fig 7a shows one minute recording from F8 side of the cortex (10/20 standard). Fig. 7a - Almost no coherence between T7 and F8 channel sites. Fig. 7b - The five second long detail of IMF4 (see fig. 7a.) 367

8 The middle subplot from Fig. 7a is the no 4 monocomponent. It represents a component from delta and theta band. The top subplot is the instantaneous frequency function. It is not a function from the current mathematical definitions textbook, but it must be seen as a sequence of consecutive frequency values (the sampling points are the set of input). The frequency range is in 0.5 to 7Hz and represent a cumulated biological events related to the F8 area. The subplot from the bottom of the figure is the instantaneous phase plot. The set of output is the [-π, π] interval. Using this iph function, in each moment of the input set (time), we can find the phase of a time moment related event. Each phase relation is from trough to next trough of the IMF. This is an accepted standard in signal processing. To have a more detailed inside of the HHT elements, we will show a shorter interval of this time series. This is the 15 to 20 seconds (five second long) interval from Fig. 7a. The details are shown in fig. 7b. The top subplot of this figure shows that the frequency happening within an IMF is almost never is a constant value (a pure harmonic oscillation). The red segments are trying to linearize part of the ifr, but it is obvious that in an interval limited by two consecutive troughs (two consecutive arrowheads and vertical blue limit lines in the middle subplot) usually there is a frequency, phase and amplitude modulation. On the bottom subplot, where the iph is presented, it is clear that usually the phase variation is not linear. We have used the green line approximation of the possible linear phase relationship between two troughs of the IMF. It is very important to consider this nonlinearity in case of the phase lock studies of biological events related to brain oscillations. To have an idea about the differences between two mono-components, also the IMF5 is presented (see fig. 8a.). IMF5 is representing a lower event structure (or IMF) of the channel F8 recording (10/20 standard). It is obvious that this is the delta oscillation of the F8 EEG channel.. Fig. 8a - The HHT of F8 EEG channel with the 5th mono-component. A detail of Fig. 8a, the length is highlighted with a red arrow. Fig 8b, on the top subplot with horizontal red lines represents a possible pure harmonic oscillation of 1Hz. Within these intervals there are frequency modulations subintervals. The phase relation is a non-linear. We have shown only few components of what HHT can provide, but our MATLAB application is calculating all of the components and also is able to provide quantitative measure of different properties of the oscillations. The HHT method can be used to analyze different origin s oscillations but it has its high efficiency in case of signals mainly coming from nonlinear and non-stationary systems. It can also be used to remove the noise (identifiable from frequency bands, see Fig. 5 as an example) without using any usual filtering procedure. This transform is a time-frequency method and the Fourier transform is not involved at all. 368

9 Fig. 8b - The 15 seconds long detail from fig. 8a. 4. Conclusions An HHT-based time frequency analysis was used to evaluate EEG signals and to present the results not only on a temporal scale but in the amplitude time frequency domain. In addition, we discuss that the characteristics of these analysis are superior to other temporal frequency results, and more information can be extracted from the characteristics of each IMF components. Using the above presented analysis methods, a clinical specialist can identify from EEG or another biological signal important messages, using the IMFs, ifr, and iph functions. Acknowledgement This work is part of the project funded by the Romanian National Authority for Scientific Research, grant No. 347/ References [1] Kianoush Nazarpour, Saeid Sanei, Leor Shoker, and Jonathon A. Chambers, Parallel space- Time-Frequency Decomposition of EEG Signals from Brain Computer Interfacing, 14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy, September 4-8, 2006, copyright by EURASIP [2] Hassan SHARABATY, Bruno JAMMES, Daniel ESTEVE, EEG analysis using HHT: One step toward automatic drowsiness scoring, 22nd International Conference on Advanced Information Networking and Applications Workshops, / IEEE [3] Rami J Oweis and Enas W Abdulhay, Seizure classification in EEG signals utilizing Hilbert- Huang transform, BioMedical Engineering OnLine 2011, 10:38, [4] Chin-Feng Lin, Shan-Wen Yeh, Yu-Yi Chien, Tsung-Ii Peng, Jung-Hua Wang and Shun- Hsyung Chang, A HHT-based Time Frequency Analysis Scheme in Clinical Alcoholic EEG Signals, WSEAS TRANSACTIONS on BIOLOGY and BIOMEDICINE, ISSN: Issue 10, Volume 5, October 2008 [5] B. Rael Cahn, John Polich, Meditation States and Traits: EEG, ERP, and Neuroimaging Studies, Psychological Bulletin Copyright 2006 by the American Psychological Association 2006, Vol. 132, No. 2, [6] Gabriel Rilling, Patrick Flandrin and Paulo Goncalves, On Empirical Mode Decomposition And Its Algorithms, Laboratoire de Physique (UMR CNRS 5672), Ecole Normale Superieure de Lyon 46, allee d Italie Lyon Cedex 07, France [7] Hualou Lianga, Steven L. Bresslerb, Robert Desimonec, Pascal Friesd, Empirical mode decomposition: a method for analyzing neural data, Neurocomputing (2005) [8] Donghoh Kim and Hee-Seok Oh, EMD: A Package for Empirical Mode Decomposition and Hilbert Spectrum, Sejong University, Korea donghoh.kim@gmail.com [9] Daubechies, I., The wavelet transform timefrequency localization and signal analysis. IEEE Trans. Inform. Theory, 36, ,