Empirical Mode Decomposition

Empirical Mode Decomposition
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On the Use of Empirical Mode Decomposition (EMD) for Alzheimer's Disease Diagnosis 1,2 1 3 Domenico Labate , Fabio La Foresta , Giuseppe Morabito , 1 1 Isabella Palamara , and Francesco Carlo Morabito 1 Department of Civil Engineering, Energy, Environment and Materials (DICEAM) Mediterranea University of Reggio Calabria, Reggio Calabria I-89060, Italy 2 DIMES – University of Calabria, Cosenza, Italy 3 University of Pavia, Pavia, Italy domenico.labate,fabio.laforesta, isabella.palamara,morabitounirc.it,peppe_mbhotmail.it Abstract. Alzheimer’s Disease (AD) is considered one of the most common form of dementia; it involves a progressive decline in cognitive function because of pa- thological modifications or damage of the brain. One of the major challenges is to develop tools for early diagnosis and disease progression. Electroencephalogram represents potentially a noninvasive and relatively non-expensive approach for screening of dementia and AD. It provides a method to objectively quantify the cortical activation patterns but it is usually considered insensitive in the early AD. This study introduces a novel method where electroencephalographic recordings (EEG) are subjected to Empirical Mode Decomposition (EMD), which decom- poses a signal into components known as Intrinsic Mode Functions (IMFs). The results, suggest that, the IMFs may be used to determine the particular frequency bandwidths in which specific phenomena occur. Keywords: EEG, Alzheimer’s Disease, Classification, EMD. 1 Introduction The brain is a highly complex and non linear system. Alzheimer Disease (AD) is the most common neurodegenerative disorder. It that involves a progressive decline in cognitive function due to atrophy of the brain as well as alteration of connectivity profiles. AD manifests itself through a slowly progressive impairment of mental func- tions whose course lasts several years 1-3. Clinically, the evaluation of memory decline is evaluated by neuropsychiatric tests (Mini Mental State Examination, MMSE) but age and education can compromise results. Some images techniques like Positron Emission Tomography (PET), Single Photon Emission Computed Tomogra- phy (SPECT), Magnetic Resonance Imaging (MRI), are useful to observe structural or functional changes in neurodegenerative disorders. Unfortunately these methods are restricted due the high cost and the related dangers to the exposure to contrast agent. On the other hands the electroencephalogram (EEG) is a non invasive and simple technique and represents a powerful and relatively cheaper approach for screening of dementia and AD. In recent years, many authors have studied the characteristic of © Springer International Publishing Switzerland 2015 121 S. Bassis et al. (eds.), Recent Advances of Neural Networks Models and Applications, Smart Innovation, Systems and Technologies 37, DOI: 10.1007/978-3-319-18164-6_12 122 D. Labate et al. EEG to improve diagnostic power by making use of many different signal processing techniques 4-9. In particular, the EEG traces of AD patients typically shows three kinds of abnormalities 10-14: i) slowing, i.e., the increase of the relative power of the low frequency bands and a reduction of the individual mean and peak alpha frequency; ii) a reduction of complexity; iii) an altered synchrony of the EEG channels recordings. The use of wavelet transform has been demonstrated useful for processing of EEG signals, also because of the ability of developing a time-frequency tiling of the origi- nal time-series. As a by-product, these kinds of decompositions are suitable to highlight and thus cancel some kinds of artifacts, invariably present in EEG traces. Unfortunately, there is no general consensus on the basic wavelet function to be used and this approach requires detailed tailoring and expertise 15. Furthermore, the suit- able wavelet basis can be different for various patients or disease’s stage. In this pa- per, a relatively novel technique, namely, the Empirical Mode Decomposition (EMD), is applied in order to exploit a natural decomposition of the EEG recordings in fre- quency bands. EMD is an adaptive and fully data-driven technique which obtains the oscillatory modes present in the data, thus producing a variable number of compo- nents. This technique is able to cope with possible non linearity and non-stationarity of this physiological signal. The paper is organized as follows: in Section 2 the theoretical basis of the applied technique are provided; then, in Section 3, the experimental data are described and the obtained results are discussed. Conclusive remarks are provided in Section 4. 2 Methodology EMD allows to decompose any time series, by means of a process called the sifting algorithm 16, into a finite set of oscillatory components by exploiting both local temporal and structural characteristics of the data. 15-19These components, called “intrinsic mode functions” (IMFs), represent the oscillation modes embedded in the data. The IMFs act as a naturally derived set of basis functions for the signal. This decomposition does not require any conditions about the stationarity and the linearity of the time-series. The principle of EMD is to locally estimate a signal x(t) as a sum of a local trend, that represents the low frequency part named residual, and a local detail component, that represents the high frequency named Intrinsic Mode Function (IMF). ∑ (1) where h (t) denote the set of IMFs and r (t) is the trend within the data, also referred i n to as the last IMF or residual. By design, an IMF satisfies two basic properties: ─ in the complete data set, the number of extrema and zero crossing are exactly equal or they differ at most by one; ─ at any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero. On the Use of Empirical Mode Decomposition for Alzheimer's Disease Diagnosis 123 The first condition is similar to the narrow-band requirement and the second one is necessary to ensure that the instantaneous frequency will not have redundant fluctua- tion as induced by asymmetric waveform 12. The IMFs extraction, from real world signals, is based on the sifting algorithm 16 as shown in Fig. 1. The algorithm steps are : 1. Detect the extrema (both local maxima and minima) of x(t); 2. Connect local maxima and minima with a spline and let e (t) and e (t) the spline min max that forms the upper and lower envelope of the signal; 3. Compute the local mean envelope : r(t)= (e (t) + e (t))/2; min max 4. IMF should have zero local mean so subtract the mean envelope from the original series d(t)= x(t)-r(t) to obtain a proto-IMF; 5. Decide if the proto-IMF d(t) is an IMF by checking the two basic condition de- scribed above; 6. If d(t) is an IMF has to be subtracted from the original data and the residual is a new data to fed back to step 1 of algorithm; 7. The sifting procedure ends when the residual of step 5 is a constant, monotonic function. The last residual is considered the trend. In EMD procedure it is important to focus both on the choice of extrema, in order to avoid over-sampling issue, and on boundary conditions for the analysis of discrete time sequences. IMFs form a complete and “nearly” orthogonal basis for the original signal, in fact, different components can have parts with similar frequencies, at differ- ent time duration, but locally any two IMFs tend to be orthogonal. Fig. 1. Block diagram of Intrinsic Mode Function extraction 124 D. Labate et al. 3 Experimental Results 3.1 Data Description and Acquisition The analysis was conducted on an experimental EEG database which refers to three different groups of subjects (male and aged between 60–75 years): Healthy Control (HC), Mild Cognitive Impairment (MCI) and Alzheimer’s Disease (AD). The inclusion criteria for enrollment of patients for statistical analysis are mainly standard and at the first level are based on Mini Mental State Examination. All pa- tients are enrolled from “IRCCS - Centro Neurolesi” of Messina, Italy, within an on- going cooperation agreement. The EEG recordings have been collected according to the sites defined by the standard 10–20 international system, channels (Fp1, Fp2, F3, F4, C3, C4, P3, P4, O1, O2, F7, F8, T3, T4, T5, T6, Fz, Cz, and Pz), at a sampling rate of 256 Hz. The data are band-pass filtered between 0.5 and 32 Hz, so including the relevant bands for AD diagnosis. In the course of the experimental activity, EEG was recorded in rest condition with closed eyes (under vigilance control). 3.2 Simulation Results The analysis here presented has been carried out by using codes written by some of the authors in MATLAB environment with specific instructions without using any available tool-boxes. Different IMFs capture the properties of the original signal at different time scale and are presumably generated from different physiological me- chanisms. As shown in Figure 2, with reference to the three different classes of sub- jects, the EEG signal is decomposed by IMFs components. Five components have st IMF, and the largest been shown in the Fig. 2. The finest time scale is shown in the 1 is in the fifth one. The frequency gradually decreases moving to lower IMFs. In Fig. 3 are shown the Power Spectral Density (PSD) of the extracted IMFs. This is useful to highlight the well-known “slowing” effect related to the disease. This behavior can be clearly reflected on IMF2. Thus, IMFs power density displays evident variations across the three different classes of subjects. This behavior is, also, well shown in Figure 4 by using a logarithmic scale. To better highlight different behaviors of the extracted IMFs, four bands are used to categorize the relative PSD: δ (0-4 Hz); θ (4-8 Hz); α (8-13 Hz) and β (13-30 Hz). As shown in Figure 5 the PSDs are distributed differently for the three class of sub- jects. In δ-band the PSDs of IMF2 and IMF3 are higher in AD-subjects then both HC and MCI; in θ-band the PSD of IMF1 and IMF2 shows the same behavior unlike the PSD of IMF3 is lower than both HC and MCI. Increasing frequency (α-band and β- band) the IMF’s PSD of HC manifests higher values, and this behavior is coherent with slowing phenomena. On the Use of Empirical Mode Decomposition for Alzheimer's Disease Diagnosis 125 4 Conclusion The results here presented suggest that an adaptive data-driven method, such as EMD, can show the dynamics of EEG for the three different classes of subject corresponding to HC, MCI, and AD patients. EMD can be considered a suitable tool for diagnosis and progression of Alzheimer’s disease. A detailed analysis of IMFs may yield the possibility of analyzing the basic dynamics characteristic of the three different classes of subjects. This may offer a novel quantitative element to clinicians for evaluating the conversion of MCI patients to AD. In the future, a comparison with other time- frequency techniques will be carried out to understand the relative merits and limita- tions of different approaches. EMD - HC - F3 EMD - MCI - F3 EMD - AD - F3 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 sec sec sec Fig. 2. Empirical Mode Decomposition of EEG recording related to three class of subject (HC, MCI and AD) for F3 electrode. EEG epochs of 10 seconds duration were processed by EMD. HC MCI AD 0.1 0.1 0.1 IMF1 IMF1 IMF1 0.09 0.09 0.09 IMF2 IMF2 IMF2 IMF3 IMF3 IMF3 0.08 0.08 0.08 IMF4 IMF4 IMF4 0.07 0.07 0.07 IMF5 IMF5 IMF5 0.06 0.06 0.06 0.05 0.05 0.05 0.04 0.04 0.04 0.03 0.03 0.03 0.02 0.02 0.02 0.01 0.01 0.01 0 0 0 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 hz hz hz Fig. 3. Power Spectral Density of IMFs related to three class of subjects (HC, MCI and AD) Normalized PSD imf-5 imf-4 imf-3 imf-2 imf-1 eeg126 D. Labate et al. HC MCI AD 0.1 0.1 0.1 IMF1 IMF1 IMF1 0.09 0.09 0.09 IMF2 IMF2 IMF2 IMF3 IMF3 IMF3 0.08 0.08 0.08 IMF4 IMF4 IMF4 0.07 0.07 0.07 IMF5 IMF5 IMF5 0.06 0.06 0.06 0.05 0.05 0.05 0.04 0.04 0.04 0.03 0.03 0.03 0.02 0.02 0.02 0.01 0.01 0.01 0 0 0 0 1 0 1 0 1 10 10 10 10 10 10 Log(f) Log(f) Log(f) Fig. 4. Power Spectral Density of IMFs for the three classes of subjects (HC, MCI and AD) in logarithmic scale Delta-band Theta-band 1 1 HC HC 0.8 0.8 MCI MCI AD AD 0.6 0.6 0.4 0.4 0.2 0.2 0 0 IMF1 IMF2 IMF3 IMF4 IMF5 IMF1 IMF2 IMF3 IMF4 IMF5 Alpha-band Beta-band 1 1 HC HC 0.8 MCI 0.8 MCI AD AD 0.6 0.6 0.4 0.4 0.2 0.2 0 0 IMF1 IMF2 IMF3 IMF4 IMF5 IMF1 IMF2 IMF3 IMF4 IMF5 Fig. 5. Normalized Power Spectral Density of IMFs for the three classes of subjects (HC, MCI and AD) categorized into four bands: δ (0-4 Hz); θ (4-8 Hz); α (8-13 Hz) and β (13-30 Hz) Acknowledgments. The authors would like to thank the “IRCCS, Centro Neurolesi, Fondazione Bonino-Pulejo”, Messina, Italy, for both making available the EEG recordings and clinically supporting the investigations. Normalized PSD On the Use of Empirical Mode Decomposition for Alzheimer's Disease Diagnosis 127 References 1. Jeong, J.: EEG Dynamics in patients with Alzheimer’s disease. Clinical Neurophysiolo- gy 115, 1490–1505 (2004) 2. 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Springer, Heidelberg (2009) Effects of Artifacts Rejection on EEG Complexity in Alzheimer's Disease 1,2 1 1 Domenico Labate , Fabio La Foresta , Nadia Mammone , 1 and Francesco Carlo Morabito 1 Department of Civil Engineering, Energy, Environment and Materials (DICEAM) Mediterranea University of Reggio Calabria, Reggio Calabria I-89060, Italy 2 DIMES – University of Calabria, Cosenza, Italy domenico.labate,fabio.laforesta, nadia.mammone,morabitounirc.it Abstract. EEG complexity analysis has recently been shown to help to diag- nose Alzheimer’s Disease (AD) in the early stages. The complexity study is based on the processing of continuous artifact-free Electroencephalography (EEG). Therefore, artifact rejection is normally required because artifacts might mimic cognitive or pathologic activity and therefore bias the neurologist visual interpretation of the EEG. Furthermore, the EEG complexity analysis is strong- ly altered by artifacts. In this paper, we evaluate the effects of artifacts rejection by a promising technique, Automatic Wavelet-Independent Component Analy- sis (AWICA), on the EEG Complexity in AD patients. We also investigate the EEG complexity before and after artifact rejection through some measures based on Shannon’s Entropy, Renyi’s Entropy and Tsallis’s Entropy. Keywords: Alzheimer’s Disease, EEG Complexity, Artifact Rejection. 1 Introduction Electroencephalography (EEG) is a de facto standard methodology for recording the electrical activity generated by populations of neurons of the cerebral cortex. The major advantage of EEG is being a noninvasive way of recording the neurophysiolog- ical activity of patients: for this reason, since its discovery, it has been widely used to investigate the neurological diseases. EEG relies essentially on a multichannel cap that records the bioelectric signals generated by the brain through a set of scalp elec- trodes, according to the international 10-20 system (Fig. 1). From an information processing perspective, it represents a multivariate, non-stationary, nonlinear time series. Many authors agree that entropy has achieved a large consensus as an indicator of complexity of nonlinear signals. This assumption is the basis of the complexity study of EEG that aims to differen- tiate among different brain states through the estimation of entropic measures. In par- ticular, there are dynamical changes of EEG related to normal aging and some others that might reveal aging pathologies. Recent works have shown that the EEG complex- ity analysis could detect markers of Alzheimer’s Disease (AD) in the EEG even in the © Springer International Publishing Switzerland 2015 129 S. Bassis et al. (eds.), Recent Advances of Neural Networks Models and Applications, Smart Innovation, Systems and Technologies 37, DOI: 10.1007/978-3-319-18164-6_13 130 D. Labate et al. early stages 1-9. In fact, the change in the complexity of EEG fluctuations seem to be linked to the evolution of AD disease: this link is not clear yet but there is a in- creasing evidence that the evolution of AD affects the shape of EEG. This would have a strong impact on the health system since EEG is a cheap and reproducible way to plan and carry out a screening and a follow-up of population at risk. The EEG complexity study is based on the processing of continuous artifacts-free recordings. Unfortunately, the EEG traces are often contaminated by artifacts, signals with non-cerebral origin that overlap to the brain waves. They are generated by different bioelectrical sources such as scalp muscles, eye movements and blinks, sweating, breathing, heart beat, or electrical line noise. The presence of artifacts in the EEG is troublesome and misleading because they can overlap to EEG and heavily obscure the brain waves that the physician needs to examine in order to come up with a reliable diagnosis. Furthermore, if visual inspection is not the final purpose of our analysis but EEG is meant to be processed by any algo- rithm, artifacts may distort EEG so that the output of the algorithm is not correct. More- over, even though the physician decided to discard the EEG artifact-laden segments, this would introduce unacceptable discontinuities in the EEG. In recent years, many authors 10-14 dealt with the problem of automatic EEG artifact rejection in order to skip the visual inspection and the subsequent manual arti- fact rejection from the EEG traces. Recently, Mammone et al. 11, introduced a promising automatic method for artifact rejection (AWICA) based on the joint use of Discrete Wavelet Transform (DWT) and Independent Component Analysis (ICA). AWICA is based on the projection of of the single EEG signal into the four frequency bands (delta, theta, alpha and beta) that are then passed through ICA. In this paper we evaluate the effects of artifact rejection by AWICA on the EEG Complexity in AD patients. In particular, we show that most of artifacts can be re- moved by AWICA. We also investigate the EEG complexity before and after artifacts rejection through entropic measures based on Shannon’s Entropy (SE), Renyi’s Entropy (RE) and Tsallis’s Entropy (TE). Fig. 1. The international 10-20 system seen from (A) left and (B) above the head. A = Ear lobe, C = central, Pg = nasopharyngeal, P = parietal, F = frontal, Fp = frontal polar, O = occipital Effects of Artifacts Rejection on EEG Complexity in Alzheimer's Disease 131 The paper is organized as follows: in Section 2 and 3 we provide a basic descrip- tion respectively of the Alzheimer's Disease and the AWICA methodology to perform artifacts rejection. In Section 4 we show the results about the effects of artifacts rejection on EEG complexity. Conclusive remarks are provided in Section 5. 2 Effects of Alzheimer's Disease on EEG Neurodegenerative diseases such as Alzheimer's Disease (AD) have long been the focus of bioengineering researches. Recently, the number of people suffering from AD is estimated in 35 million and the number is expected to raise to 110 million by the year 2050. As the number of elderly population affected by AD rises, the need for making available to the community innovative, accurate, inexpensive and non- invasive diagnostic techniques for early screening of population at risk is becoming a relevantly urgent public health concern 15, 16. Many researches have shown that the EEG of patients suffering from AD start to modify well in advance of the clinical diagnosis. Furthermore, there are even condi- tions and diseases that can mimic AD symptoms which are instead reversible. Early diagnosis would be of great importance. As of today, a definitive diagnosis of Alz- heimer's is possible only by postmortem necropsy. It is usually diagnosed clinically from the patient history, collateral history from relatives, and clinical observations, based on the presence of characteristic neurological and neuropsychological features and the absence of alternative conditions 17. Advanced medical imaging with com- puted tomography (CT) or magnetic resonance imaging (MRI), as well as with single photon emission computed tomography (SPECT) or positron emission tomography (PET) can be used to help exclude other cerebral pathology or subtypes of dementia. However, this kinds of diagnostics are not suitable for screening of large populations. A non-invasive alternative clinical diagnosis is represented by EEG. AD is known to have three main effects on EEG 4, 18: 1. slowing, i.e. the increase of the relative power of the low frequency bands (delta, 0.5-4 Hz, and theta, 4-8 Hz), coupled with a reduction of the mean frequency (this can be measured by standard Fourier analysis); 2. complexity reduction, by implicitly hypothesizing that regularity of the AD patients’ EEG is higher than age-matched controls; 3. loss of synchrony of the electrodes’ time series reading: this effect on syn- chrony can be measured by both nonlinear and linear indices. Recent studies also give a dynamical description of AD development, data from AD patients showed a loss of complexity over the wide range of time scales, indicat- ing a destruction of nonlinear structures in brain dynamics 1, 9. These studies was conducted only on artifacts-free EEG segments by cutting the entire artifactual EEG segments. In the next sections, we try to perform the EEG complexity analysis after artifacts rejection procedure and we evaluate the effects through entropic measures. 132 D. Labate et al. 3 AWICA Methodology for Artifacts Rejection The AWICA methodology is based on the exploitation of the different information content in the four frequency bands (rhythms) obtained by the DWT step that pre- cedes ICA 11. The method consists in a two-step artifact identification procedure based on the estimation of kurtosis and Renyi’s entropy 19. The DWT allows to completely recover the neural components of the EEG channels corrupted by the arti- facts outside of the contaminated frequency range. AWICA also mostly preserves the cerebral activity because of the increased redundancy of the input to the ICA-step. The block diagram of AWICA is depicted in Fig. 2: (1) the first level is a decom- position through the Discrete Wavelet Transform (DWT) that partitions each channel of the original dataset into the four major bands of brain activity; each rhythm of each channel is represented by a Wavelet Component (WC). (2) Once the raw data record- ings have been so projected into the dimensional space, the Wavelet Components (WCs) linked to artifactual events are automatically identified by means of a quantita- tive measure and (3) passed through ICA in order to concentrate the artifactual con- tent in a few independent components. (4) Then, the artifactual Wavelet Independent Components (WICs) are automatically selected and rejected. (5) Two reconstruction steps are then performed: the inverse ICA and the inverse DWT, so that the artifact- free EEG dataset is eventually reconstructed (for more details see 11). As shown in the next section, AWICA methodology was successfully applied on the artifact-corrupted EEG segments. In addition, the possible alteration of EEG Complexity was evaluated. Fig. 2. Block diagram of WICA processing system for EEG artifacts rejection Effects of Artifacts Rejection on EEG Complexity in Alzheimer's Disease 133 4 Results The analysis was conducted on an experimental EEG database which refers to three different groups of subjects (male and aged between 60–75 years): Mild Cognitive Impaired (MCI) patients, AD patients and age-matched healthy elderly control (HC). The inclusion criteria for enrollment of patients for statistical analysis are mainly standard and at the first level are based on Mini Mental State Examination. The EEG database has been made available by the IRCCS “Centro Neurolesi” of Messina, Italy, within an ongoing cooperation agreement. The EEG recordings have been col-lected according to the sites defined by the standard 10–20 international system, 19-channels (Fp1, Fp2, F3, F4, C3, C4, P3, P4, O1, O2, F7, F8, T3, T4, T5, T6, Fz, Cz, and Pz), at a sampling rate of 256 Hz. The data are band-pass filtered between 0.5 and 32 Hz, so including the relevant bands for AD diagnosis. In the course of the experimental ac- tivity, EEG was recorded in rest condition with closed eyes (under vigilance control). The continuous EEG, whose length is 210 seconds, was partitioned into 21 windows of 10 seconds each. Fig. 3 shows the 12nd window, that was the only time window corrupted by artifacts (on the 7th channel). The artifact was successfully removed by AWICA methodology and the artifact-free continuous EEG was reconstructed. Mammone et al. 11 have shown that the artifact rejection performed by AWICA did not introduce significant alterations in the spectrum and the temporal correlation of the EEG. But the AWICA methodology effects on the EEG complexity have not been evaluated. Morabito et al. 4 have shown that entropy can be successfully employed to estimate the EEG complexity. Thus, the entropic indexes based on Shannon’s Entropy (SE), Renyi’s Entropy (RE) and Tsallis’s Entropy (TE) were estimated to evaluate the effects on the EEG complexity (for more details about entropic indexes see 1). th In Fig. 4 we compare the normalized RE, SE and TE of each channels of the 12 window before (red line) and after (green line) artifact rejection with the mean values of normalized RE, SE and TE of each channels computed on the artifact-free win- th dows (blue line). All entropic indexes of P3 (7 channel) are corrupted by the artifact. The AWICA artifact rejection is able to remove the alteration of all entropic indexes restoring the measures into mean-value range. 5 Conclusions The recently introduced entropic complexity measures has been shown to be capable of processing EEG data as an enabling tool for distinguish among different brain states. These indexes are also able to capture the typical “slowing effect” related to Alzheimer’s disease. It has been shown that entropic indexes are particularly suitable for monitoring the changes in the elderly brain by distinguish between physiological ageing and pathological dementias. In this paper we have also evaluated the effects of the artifacts rejection by AWICA methodology on the entropic indexes that are em- ployed in the EEG complexity analysis. The results confirm that AWICA is able to rectify the entropy value alteration. 134 D. Labate et al. Fig. 3. Multichannel real EEG recorded from an AD patient. According to the international 10- 20 system, the montage is Fp1, Fp2, F3, F4, C3, C4, P3, P4, O1, O2, F7, F8, T3, T4, T5, T6, Fz, Cz, and Pz. In particular, the 12nd window is shown, that was the only one corrupted by artifacts. (Top) The EEG showing an artifact on the 7th electrode (P3). (Bottom) The same EEG segment after artifact rejection through AWICA. Effects of Artifacts Rejection on EEG Complexity in Alzheimer's Disease 135 Fig. 4. Evaluation of EEG complexity by normalized Entropic Measures. Comparison of nor- nd malized RE, SE and TE of each channels of the 12 window before (red line) and after (green line) artifact rejection with the mean values of normalized RE, SE and TE of each channels computed on the artifact-free windows (blue line). Acknowledgments. The authors would like to thank the “IRCCS, Centro Neurolesi, Fondazione Bonino-Pulejo”, Messina, Italy, for both making available the EEG re- cordings and clinically supporting the investigations. References 1. 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In: Proceedings of the 2007 International Conference on Information Acquisition (ICIA 2007), article number 4295725, pp. 195–200 (2007) Denoising Magnetotelluric Recordings Using Self-Organizing Maps 1 1 1 2 Luca D’Auria , Antonietta M. Esposito , Zaccaria Petrillo , and Agata Siniscalchi 1 Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Napoli Osservatorio Vesuviano, Napoli, Italy luca.dauria,antonietta.esposito,zaccaria.petrilloingv.it 2 Università degli Studi di Bari “Aldo Moro”, Dipartimento di Scienze della Terra e Geoambientali, Bari, Italy agata.siniscalchiuniba.it Abstract. A novel approach for processing magnetotelluric data in urban areas is presented. The magnetotelluric (MT) method is a valid technique for geophysical exploration of the Earth’s interiors. It provides information about the rocks’ resistivity and in particular, in volcanology, it allows to delineate the complex structure of volcanoes possibly detecting magmatic chambers and hydrothermal systems. Indeed, geological fluids (e.g. magma) are characterized by resistivity of many orders of magnitude lower than the surrounding rocks. However, the MT method requires the presence of natural electromagnetic fields. So in urban areas, the noise strongly influences the MT recordings, especially that produced by trains. Various denoising techniques have been proposed, but it is not always easy to identify the noise-free intervals. Thus, in this work a neural method, the Self-Organizing Map (SOM), is proposed to perform the clustering of impedance tensors, computed on a Discrete Wavelet (DW) expansion of MT recordings. The use of the DW transform is motivated by the need of analyzing MT recordings both in time and frequency domain. The SOM is principally tested on synthetic dataset. Then, as a further validation of the method, it is applied on real data recorded at volcano Etna, Sicily. In both cases, the obtained results have shown the SOM capability of greatly reducing the effect of the noise on the retrieved apparent resistivity curves. Keywords: magnetotelluric method (MT), denoising, SOM networks. 1 The Magnetotelluric (MT) Method The Magnetotelluric (MT) method 22 is based on the study of the interaction between natural low frequency electromagnetic waves and the rocks in the Earth’s interiors. The simultaneous recording at the Earth surface of the electric and the magnetic fields allows the determination of the resistivity of rocks inside the Earth. MT signals span a wide range of frequencies: the sources of the high frequency (1÷105 Hz) are lightning while the low frequency source (10-5÷1 Hz) is the © Springer International Publishing Switzerland 2015 137 S. Bassis et al. (eds.), Recent Advances of Neural Networks Models and Applications, Smart Innovation, Systems and Technologies 37, DOI: 10.1007/978-3-319-18164-6_14 138 L. D’Auria et al. interaction of the solar wind with the magnetosphere and the ionosphere. Both sources realize on the Earth surface a quasi-plane wave orthogonally incident. Figure 1 illustrates a schematic representation of the physics of magnetotelluric exploration while figure 2 shows how the MT instrumentation operates. Fig. 1. A scheme of physics of magnetotelluric exploration Fig. 2. The MT instrumentation The physical basis of the method relies on the relationship between the electric and the magnetic fields measured on the Earth surface: E = ZH, where E is the electric field vector, H is the magnetic field vector and Z is the impedance tensor. Due to the high atmosphere resistivity, the vertical component of the electric field is close to zero. Hence only the horizontal components of the vectors E and H are usually considered. This implies that a 2x2 complex matrix represents the impedance tensor Z. Natural oscillations of the magnetic field, triggered by various sources (e.g. solar wind transients, thunders, etc) provide a broad spectrum of natural signals useful for MT studies. They excite currents within the Earth (called telluric currents, from Denoising Magnetotelluric Recordings Using Self-Organizing Maps 139 which the name magnetotelluric method comes), which are the source of an electric field, whose intensity depends upon the resistivity of the rocks. The longer the period of the oscillation, the deeper is the resistivity investigated. Signals with a period of 5 10 s allow the determination of the Earth resistivity up to tens of kilometers beneath -2 the surface. The other end of the spectrum signals with a period of 10 s determines accurately the resistivity of the rocks up to depth of few hundreds meters. The full determination of the resistivity as a function of the depth requires studying the whole range of MT signal frequencies. The basic assumption of the MT method is that the electromagnetic field, used for the analysis, consists in downgoing plane waves with nearly vertical incidence. This assumption is usually valid when dealing with natural sources. However, in urbanized areas, artificial noise could affect MT analysis dramatically, especially when dealing 2 with periods longer than 10 s (i.e. with depth higher than few kilometers). The main noise sources are trains, whose electromagnetic field is so powerful to disturb MT recording many kilometers away from their path. Different techniques for MT recording denoising have been proposed. They are usually based on searching for specific signatures in the MT recordings indicating the presence of noise. For instance, recently Escalas et al. (2013) proposed a technique based on the analysis of the polarization of the electric field to detect and remove linearly polarized portions of MT signals, which are likely to be affected by noise due to human settlements and infrastructures therein. In this work a novel technique based on the clustering of impedance tensors, computed on a Discrete Wavelet (DW) expansion of MT recordings, is proposed. The DW transform allows analyzing MT recordings both in time and frequency domains 11. In the following, the data processing performed on synthetic and real data is described and the applied clustering technique is illustrated. Finally the SOM results are discussed. 2 Data Processing The MT method has been applied on synthetic data generated by an automatic procedure, assuming the use of a single recording station. The signals are corrupted by adding different noise levels in order to provide different noise conditions. As an example, figure 3 shows a MT synthetic noisy signal and its components in the magnetic and electric filed. Figure 4 visualizes instead a real MT signal recorded at the volcano Etna, Sicily. To exploit the information about the phase difference of the signals we use their analytic representation: A = s(t) + iHs(t) where s(t) is the time domain signal, H is the Hilbert transform and i is the imaginary unit. Once DW transformed, the electric and magnetic components of the MT signal are processed separately for each wavelet scale. Given a set of coefficients 140 L. D’Auria et al. the impedance tensor is determined through the least squares solution of the linear system of equations in (1): E = Z H + Z H xi xx xi xy yi (1) E = Z H + Z H yi yx xi yy yi ' where the index i runs over the DW coefficients of the analytic representation of the fields for a given wavelet scale. However, the application of the previous procedure to a noisy dataset is likely to lead to unreliable results. Fig. 3. An example of a synthetic MT signal where noise (N/S 50%) has been added to almost 30% of it. Hx and Hy are the components of the magnetic field while Ex and Ey the components of the electric field. Being the most relevant noise sources transient, the basic idea of the method is to apply a clustering procedure of the retrieved impedance tensors over subsets of the s DW coefficients for each wavelet scale. A set of 2 DW coefficients for a wavelet scale s can be partitioned in different ways. We have applied a Monte Carlo technique selecting N random subsets of k coefficients from the whole set. For each set we applied the least square approach of eq. (1) to determine a set of impedance tensors. Finally, the obtained impedance vectors have been normalized using a logistic transformation which scales all possible values between 0,1 before being processed by the SOM.

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