Multivariate Empirical Mode Decomposition Research Articles

A joint framework for multivariate signal denoising using multivariate empirical mode decomposition

In this paper, a novel multivariate denoising scheme using multivariate empirical mode decomposition (MEMD) is proposed. Unlike previous EMD-based denoising methods, the proposed scheme can align common frequency modes across multiple channels of a multivariate data, thus, facilitating direct multichannel data denoising. The key idea in this work is to extend our earlier MEMD based denoising method for univariate signal in Hao et al. (2016) [19] to the multivariate data. The MEMD modes (known as intrinsic mode functions) for separating noise components are first adaptively selected on the basis of a similarity measure between the probability density function (pdf) of the input multivariate signal and that of each mode by Frobenius norm. The selected modes are then denoised further by a local interval thesholding procedure followed by reconstruction of the thresholded IMFs. The resulting method operates directly in multidimensional space where input signal resides, owing to MEMD, and also benefits from its mode-alignment property. Furthermore, subspace projection is introduced within the framework of the proposed method to exploit the inter-channel dependence among IMFs with the same index, enabling the diversity reception of the signal. Performance of the proposed method against standard multiscale denoising schemes is demonstrated on both synthetic and real world data.

GPU-Accelerated Multivariate Empirical Mode Decomposition for Massive Neural Data Processing

This paper presents an efficient implementation of multivariate empirical mode decomposition (MEMD) algorithm, a multivariate extension of EMD algorithm. Analogous to EMD, MEMD decomposes a multivariate signal into its intrinsic mode functions using joint rotational mode. The algorithm is computationally intensive because of its recursive nature and any increase in input data size results in a non-linear increase in its execution time. Therefore, it is extremely time-consuming to obtain a decomposition of signal, such as EEG into its intrinsic modes using MEMD. As the interest in applying MEMD algorithm in various domains is increasing, there is a need to develop an optimized implementation of the algorithm, since it requires repeated execution of the same operations and computationally extensive interpolations on each projected vector. This can be done using GPGPU, because it has the power to process similar function on different blocks of data. We have compared the optimized implementation of MEMD, using GPU, with the MATLAB implementation for hexa-variate and hexa-deca-variate data sets, and observed that the GPU-based optimized implementation results in approximately $6\times \sim 16\times $ performance improvements in terms of time consumption.

Evaluation of joint analysis of multiple interictal events for spike extraction and source imaging

Interictal spike extraction and epileptic source localisation is an important neuroimaging problem. Manual analysis of EEG interictal spikes is time-consuming and imposes an overwhelming workload for the physician. To overcome this problem, we investigate a joint analysis of EEG interictal events and automatic spike extraction for epileptic source localisation. In this work, Multivariate Empirical Mode Decomposition (MEMD) is applied to each event separately and the Intrinsic Mode Functions (IMFs) are extracted. The joint analysis combines IMFs of different interictal events to a common empirical mode domain. A power threshold step recovers the interictal spikes in the joint signal by filtering the background EEG activity and the noises. Experimental analysis of four epileptic patient data set shows that the filtered EEG signal indicates a significant improvement in the Signal to Noise Ratio (SNR) (p < 0.0047(t-test), min: 35.3283 dB and max: 52.2506 dB). The results of this paper show a good conformance (concordance rate, min:40% and max:80%) in localising the epileptogenic regions.

Improved spectrum analysis in EEG for measure of depth of anesthesia based on phase-rectified signal averaging

The definition of the depth of anesthesia (DOA) is still controversial and its measurement is not completely standardized in modern anesthesia. Power spectral analysis is an important method for feature detection in electroencephalogram (EEG) signals. Several spectral parameters derived from EEG have been proposed for measuring DOA in clinical applications. In the present paper, an improved method based on phase-rectified signal averaging (PRSA) is designed to improve the predictive accuracy of relative alpha and beta power, a frequency band power ratio, total power, median frequency (MF), spectral edge frequency 95 (SEF95), and spectral entropy for assessing anesthetic drug effects. Fifty-six patients undergoing general anesthesia in an operating theatre are studied. All EEG signals are continuously recorded from the awake state to the end of the recovery state and then filtered using multivariate empirical mode decomposition (MEMD). All parameters are evaluated using the commercial bispectral index (BIS) and expert assessment of conscious level (EACL), respectively. The ability to predict DOA is estimated using the area under the receiver-operator characteristics curve (AUC). All indicators based on the improved method can clearly discriminate the conscious state from the anesthetized state after filtration (p < 0.05). A significantly larger mean AUC (p < 0.05) shows that the improved method performs better than the conventional method to measure the DOA in most circumstances. Especially for raw EEG contaminated by artifacts, when the BIS index is used to indicate the consciousness level, the improvement is 7.37% (p < 0.05), 9.04% (p < 0.05), 18.46% (p < 0.05), 27.73% (p < 0.05), 14.65% (p < 0.05), 2.52%, 5.38% and 6.24% (p < 0.05) for relative alpha and beta power, power ratio, total power, MF, SEF, RE and SE, respectively. However, when the EACL is used to indicate the consciousness level, the improvement is 3.30% (p < 0.05), 16.69% (p < 0.05), 15.08% (p < 0.05), 34.83% (p < 0.05), 27.78% (p < 0.05), 5.89% (p < 0.05), 26.05% (p < 0.05) and 23.42% (p < 0.05). Spectral parameters derived from PRSA are more useful to measure the DOA in noisy cases.

EEG artifacts reduction by multivariate empirical mode decomposition and multiscale entropy for monitoring depth of anaesthesia during surgery.

Electroencephalography (EEG) has been widely utilized to measure the depth of anaesthesia (DOA) during operation. However, the EEG signals are usually contaminated by artifacts which have a consequence on the measured DOA accuracy. In this study, an effective and useful filtering algorithm based on multivariate empirical mode decomposition and multiscale entropy (MSE) is proposed to measure DOA. Mean entropy of MSE is used as an index to find artifacts-free intrinsic mode functions. The effect of different levels of artifacts on the performances of the proposed filtering is analysed using simulated data. Furthermore, 21 patients' EEG signals are collected and analysed using sample entropy to calculate the complexity for monitoring DOA. The correlation coefficients of entropy and bispectral index (BIS) results show 0.14±0.30 and 0.63±0.09 before and after filtering, respectively. Artificial neural network (ANN) model is used for range mapping in order to correlate the measurements with BIS. The ANN method results show strong correlation coefficient (0.75±0.08). The results in this paper verify that entropy values and BIS have a strong correlation for the purpose of DOA monitoring and the proposed filtering method can effectively filter artifacts from EEG signals. The proposed method performs better than the commonly used wavelet denoising method. This study provides a fully adaptive and automated filter for EEG to measure DOA more accuracy and thus reduce risk related to maintenance of anaesthetic agents.

A Novel Approach for the Analysis of Multi-Channel EEG Signal using Advance Technique

Objectives: In this research paper, Electroencephalogram (EEG) is recorded by placing electrodes on the scalp for different mental task. The significant features are extracted for three different metal tasks as mental arithmetic, baseline and letter composing. Methods/Statistical analysis: In the EEG signals, there are many features which having some significant information and some having false. The significant features are extracted by using advance techniques as Multivariate Empirical Mode Decomposition (MEMD) and Hilbert-Huang Transform (HHT). The t-paired test is used for determining the discrimination power of extracted features. Findings: After applying MEMD techniques we have achieved twelve multivariate Intrinsic Mode Functions (IMFs) and one residue. Most sensitive IMFs are selected by calculating Power Spectral Density (PSD) of each IMFs functions by Welch method. The Instantaneous Amplitude (IA) and Instantaneous Phase (IP) from most sensitive IMF are investigated by using Hilbert Huang transform (HHT) and features such as min., max., Skewness and kurtosis are extracted from IA and IP. The feature values are tested for their class discrimination power (p< .05) using paired t test. The results of paired t test support their applicability to be used as feature vector for any classification application. Accuracy nearby 80% to 90% is procured for different mental task EEG signals by using these extracted features. Application/Improvements: The investigated results are applicable for Brain Computer Interface. If a handicapped person (his hands and legs are not working/living) wants to write some letters on the screen of a desktop, so by putting the electrode on scalp and by measuring the electrical signals of his/her brain through EEG, we can apply these significant features for converting the electrical signals in to letters with the help of computer. In this research, we have investigated only linear feature, so further research area is open for investigating of Non-linear features of EEG signals.

Random eye state change detection in real-time using EEG signals

Maximum and minimum computed across channels is used to monitor the Electroencephalogram signals for possible change of the eye state. Upon detection of a possible change, the last two seconds of the signal is passed through Multivariate Empirical Mode Decomposition and relevant features are extracted. The features are then fed into Logistic Regression and Artificial Neural Network classifiers to confirm the eye state change. The proposed algorithm detects the eye state change with 88.2% accuracy in less than two seconds. This provides a valuable improvement in comparison to a recent procedure that takes about 20 minutes to classify new instances with 97.3% accuracy. The introduced algorithm is promising in the real-time eye state classification as increasing the training examples would increase its accuracy.

Integration of multivariate empirical mode decomposition and independent component analysis for fetal ECG separation from abdominal signals.

The fetal electrocardiogram (FECG) signals are essential to monitor the health condition of the baby. Fetal heart rate (FHR) is commonly used for diagnosing certain abnormalities in the formation of the heart. Usually, non-invasive abdominal electrocardiogram (AbECG) signals are obtained by placing surface electrodes in the abdomen region of the pregnant woman. AbECG signals are often not suitable for the direct analysis of fetal heart activity. Moreover, the strength and magnitude of the FECG signals are low compared to the maternal electrocardiogram (MECG) signals. The MECG signals are often superimposed with the FECG signals that make the monitoring of FECG signals a difficult task. Primary goal of the paper is to separate the fetal electrocardiogram (FECG) signals from the unwanted maternal electrocardiogram (MECG) signals. A multivariate signal processing procedure is proposed here that combines the Multivariate Empirical Mode Decomposition (MEMD) and Independent Component Analysis (ICA). The proposed method is evaluated with clinical abdominal signals taken from three pregnant women (N= 3) recorded during the 38-41 weeks of the gestation period. The number of fetal R-wave detected (NEFQRS), the number of unwanted maternal peaks (NMQRS), the number of undetected fetal R-wave (NUFQRS) and the FHR detection accuracy quantifies the performance of our method. Clinical investigation with three test subjects shows an overall detection accuracy of 92.8%. Comparative analysis with benchmark signal processing method such as ICA suggests the noteworthy performance of our method.

Estimation of Brain Connectivity during Motor Imagery Tasks using Noise-Assisted Multivariate Empirical Mode Decomposition

The neural dynamics underlying the causal network during motor planning or imagery in the human brain are not well understood. The lack of signal processing tools suitable for the analysis of nonlinear and nonstationary electroencephalographic (EEG) hinders such analyses. In this study, noiseassisted multivariate empirical mode decomposition (NA-MEMD) is used to estimate the causal inference in the frequency domain, i.e., partial directed coherence (PDC). Natural and intrinsic oscillations corresponding to the motor imagery tasks can be extracted due to the data-driven approach of NA-MEMD, which does not employ predefined basis functions. Simulations based on synthetic data with a time delay between two signals demonstrated that NA-MEMD was the optimal method for estimating the delay between two signals. Furthermore, classification analysis of the motor imagery responses of 29 subjects revealed that NA-MEMD is a prerequisite process for estimating the causal network across multichannel EEG data during mental tasks.

Multi-scale correlations between soil hydraulic properties and associated factors along a Brazilian watershed transect

Soil hydraulic properties are important to the understanding and modeling of hydrological processes at the watershed scale. These properties are presumed to be correlated with associated topographic attributes and other soil factors operating at different intensities and scales. Using multivariate empirical mode decomposition (MEMD), this study examined the multi-scale correlations among two soil hydraulic properties and two topographic attributes and three soil factors along a transect in the Pelotas River Watershed (PRW) situated in Southern Brazil. Soil water content at field capacity (θFC) and saturated hydraulic conductivity (KS) were determined for 100 soil samples taken at 250-m intervals along a 25-km transect that cut through the PRW. The five selected factors were elevation (Ele), slope (Slo), sand content (Sand), bulk density (Bd), and soil organic carbon (SOC). The topographic attributes were derived from a digital elevation model, while those related to soils were determined for the collected samples. The multivariate data series of the two soil hydraulic properties and five associated factors were decomposed into six intrinsic mode functions (IMFs). For θFC, 52.4% of the total variance was separated at IMF1 (scale of 728m) and IMF2 (1,113m), while for ln KS, 35.9% of the variance was separated at IMF1 (728m) and IMF6 (scale of 11,877m). It was found that scale-specific relationships between soil hydraulic properties and the associated factors varied with scale. The associated factors exerted influence on the soil hydraulic properties at their own dominant scale(s). The θFC and ln KS values at each IMF (specific scale) and residue were predicted from the scale-specific associated factors at the same IMF or residue. The total of all the predicted IMFs including the residue was then used to predict the θFC and ln KS at the measurement scale. Sand had the greatest relative importance to the measurement-scale θFC prediction model, while topographic properties were clearly the dominant explanatory factors for the overall ln KS prediction. The overall ln KS predictions using the MEMD outperformed those based on the original data.

Application of Noise-Assisted Multivariate Empirical Mode Decomposition in VLF-EM Data to Identify Underground River

Very low-frequency electromagnetic (VLF-EM) method can be used for imaging the subsurface resistivity, where this image can be used directly to determine subsurface condition. VLF-EM data are generally contaminated with unwanted noise which often leads to a mistake in the resistivity imaging result. In this study, noise-assisted multivariate empirical mode decomposition (NA-MEMD) was applied to reject the unwanted noise contained within the VLF-EM data which produced NA-MEMD-filtered VLF-EM data. The resistivity imaging resulted by filtered VLF-EM data has been used for determining the position of underground rivers over the karst area of Gunung Kidul district, Central Java province, Indonesia. The results show that the NA-MEMD-filtered VLF-EM data were more accurate in determining underground river tracks of the Suci cave areas. The overall result was supported by qualitative analyses (Fraser and K–Hjelt filters) of observed VLF-EM data as well as the NA-MEMD-filtered VLF-EM data.

EEG-Based Prediction of Epileptic Seizures Using Phase Synchronization Elicited from Noise-Assisted Multivariate Empirical Mode Decomposition

In this study, we examined the phase locking value (PLV) for seizure prediction, particularly, in the gamma frequency band. We prepared simulation data and 65 clinical cases of seizure. In addition, various filtering algorithms including bandpass filtering, empirical mode decomposition, multivariate empirical mode decomposition and noise-assisted multivariate empirical mode decomposition (NA-MEMD) were used to decompose spectral components from the data. Moreover, in the case of clinical data, the PLVs were used to classify between interictal and preictal stages using a support vector machine. The highest PLV was achieved with NA-MEMD with 0-dB white noise algorithm (0.9988), which exhibited statistically significant differences compared to other filtering algorithms. Moreover, the classification rate was the highest for the NA-MEMD with 0-dB algorithm (83.17%). In terms of frequency components, examining the gamma band resulted in the highest classification rates for all algorithms, compared to other frequency bands such as theta, alpha, and beta bands. We found that PLVs calculated with the NA-MEMD algorithm could be used as a potential biological marker for seizure prediction. Moreover, the gamma frequency band was useful for discriminating between interictal and preictal stages.

Analyzing the Hydroclimatic Teleconnections of Summer Monsoon Rainfall in Kerala, India, Using Multivariate Empirical Mode Decomposition and Time-Dependent Intrinsic Correlation

This letter presents an alternative approach for investigating the teleconnections of summer monsoon rainfall in the state of Kerala, India, with four prominent climatic oscillations in multiple time scales based on multivariate empirical mode decomposition (EMD) (MEMD) and time-dependent intrinsic correlation (TDIC). First, the multivariate data set constituting summer monsoon rainfall time series and the climate oscillations such as the Quasi-Biennial Oscillation, El Nino Southern Oscillation (ENSO), Atlantic Multidecadal Oscillation, and Equatorial Indian Ocean Oscillation are decomposed to several rotational modes by employing MEMD. To capture the associations in shorter time spells, the TDIC method is employed, in which the sliding window is adaptively fixed based on instantaneous periods obtained by the Hilbert transform of the obtained modes. From the analysis, it is found that the strength and nature of association between summer monsoon rainfall and the climate oscillations vary with time scales and time spells. The performance of MEMD-based TDIC analysis is compared with that of EMD-based TDIC, and it was found that the former one well captured the direct correlation between ENSO and summer monsoon rainfall in the 1997–1998 period and the opposing correlation in the 2002–2003 period, while the latter approach failed to capture such associations properly.

Technical note: Multiple wavelet coherence for untangling scale-specific and localized multivariate relationships in geosciences

Abstract. The scale-specific and localized bivariate relationships in geosciences can be revealed using bivariate wavelet coherence. The objective of this study was to develop a multiple wavelet coherence method for examining scale-specific and localized multivariate relationships. Stationary and non-stationary artificial data sets, generated with the response variable as the summation of five predictor variables (cosine waves) with different scales, were used to test the new method. Comparisons were also conducted using existing multivariate methods, including multiple spectral coherence and multivariate empirical mode decomposition (MEMD). Results show that multiple spectral coherence is unable to identify localized multivariate relationships, and underestimates the scale-specific multivariate relationships for non-stationary processes. The MEMD method was able to separate all variables into components at the same set of scales, revealing scale-specific relationships when combined with multiple correlation coefficients, but has the same weakness as multiple spectral coherence. However, multiple wavelet coherences are able to identify scale-specific and localized multivariate relationships, as they are close to 1 at multiple scales and locations corresponding to those of predictor variables. Therefore, multiple wavelet coherence outperforms other common multivariate methods. Multiple wavelet coherence was applied to a real data set and revealed the optimal combination of factors for explaining temporal variation of free water evaporation at the Changwu site in China at multiple scale-location domains. Matlab codes for multiple wavelet coherence were developed and are provided in the Supplement.

A method of eliminating the vibration signal noise of hydropower unit based on NA-MEMD and approximate entropy

A new vibration signal denoising method of hydropower unit based on noise-assisted multivariate empirical mode decomposition (NA-MEMD) and approximate entropy is proposed. Firstly, the NA-MEMD is used to decompose the signal into a number of intrinsic mode functions. Then, the approximate entropy of each component is computed. According to a preset threshold of approximate entropy, these components are reconstructed to denoise vibration signal of hydropower unit. The analysis results of simulation signal and real-world signal show that the proposed method is adaptive and has a good denoising performance. It is very suitable for online denoising of hydropower unit's vibration signal.

MEMD-enhanced multivariate fuzzy entropy for the evaluation of complexity in biomedical signals.

Multivariate multiscale entropy (mvMSE) has been proposed as a combination of the coarse-graining process and multivariate sample entropy (mvSE) to quantify the irregularity of multivariate signals. However, both the coarse-graining process and mvSE may not be reliable for short signals. Although the coarse-graining process can be replaced with multivariate empirical mode decomposition (MEMD), the relative instability of mvSE for short signals remains a problem. Here, we address this issue by proposing the multivariate fuzzy entropy (mvFE) with a new fuzzy membership function. The results using white Gaussian noise show that the mvFE leads to more reliable and stable results, especially for short signals, in comparison with mvSE. Accordingly, we propose MEMD-enhanced mvFE to quantify the complexity of signals. The characteristics of brain regions influenced by partial epilepsy are investigated by focal and non-focal electroencephalogram (EEG) time series. In this sense, the proposed MEMD-enhanced mvFE and mvSE are employed to discriminate focal EEG signals from non-focal ones. The results demonstrate the MEMD-enhanced mvFE values have a smaller coefficient of variation in comparison with those obtained by the MEMD-enhanced mvSE, even for long signals. The results also show that the MEMD-enhanced mvFE has better performance to quantify focal and non-focal signals compared with multivariate multiscale permutation entropy.

GPR investigation of the near-surface geology in a geothermal river valley using contemporary data decomposition techniques with forward simulation modeling

Although geophysical studies on the geothermal field are in favor of deep structures, the shallow investigations are needed for understanding the local hydrological regime and assessing environmental compliance when setting up a geothermal power plant. We demonstrate the possibility of investigating the shallow structure of a complex site of the geothermal valley located at Chingshui, northeast Taiwan by using the ground penetrating radar (GPR) with advanced data processing techniques. Taking the challenging topography into account, the low frequency (50MHz) unshielded bistatic GPR antennas were transported above the ground to prevent from submerging in water and avoid the surface obstacles. Two newly developed data processing techniques, the multidimensional ensemble empirical mode decomposition (MDEEMD) and multivariate empirical mode decomposition (MEMD), with the Hilbert-Huang spectrogram analysis were applied to the data. For each survey line, an initial subsurface layer model was generated by referring to the processed field data, and the finalized subsurface layer model accompanying the synthetic GPR profile were obtained with the aid of the finite difference time domain (FDTD) numerical simulation modeling. The results of this study suggest that the undulation reflections shown in each survey line are folding structures extending from the cliff edge, and that no evidence of fault traces near the surface is found. Apart from the geological findings, we believe that the field technique in conjunction with the proposed data processing method can overcome the topographic difficulties of the geothermal field and may provide better subsurface image of an area with poor GPR reflection quality.

Emotion recognition from EEG signals by using multivariate empirical mode decomposition

This is the artifact for the paper titled "POKER: Permutation-based SIMD Execution of Intensive Tree Search by Path Encoding" accepted at CGO 2018. This artifact helps reproduce the results presented in Figures 7 - 9 and Tables 2 - 3 in Section 4. For more information on how to use it, please refer to our paper and the README.txt file in this package. Please note that POKER is a work in progress. This artifact is a snapshot of this work and thus is only applicable under the experimental settings described in this paper. Please feel free to contact the authors if you have any questions.

Characterizing scale-specific environmental factors affecting soil organic carbon along two landscape transects.

Soil organic carbon (SOC) is one of the most important soil properties affecting many other soil and environmental properties and processes. In order to understand and manage SOC effectively, it is important to identify the scale-specific main factors affecting SOC distributions, which in this study occurred in a watershed on the Loess Plateau. Two transects were selected that passed along the upper slopes on each side of the main gully of the Liudaogou watershed. Transect 1 (3411-m length) had 27 sampling sites at 131-m intervals; transect 2 (3597m length) had 30 sampling sites at 124-m intervals. The two transects were chosen in order to compare landscape patterns of differing complexity that were in close proximity, which reduced the effects of factors that would be caused by different locations. The landscape of transect 1 was more complex due to the greater diversity in cultivation. Multivariate empirical mode decomposition (MEMD) decomposed the total variation in SOC and five selected environmental factors into four intrinsic mode functions (IMFs) and a residual according to the scale of occurrence. Scale-specific correlation analysis was used to identify significant relationships between SOC and the environmental factors. The dominant scales were those that were the largest contributors to the total SOC variance; for transect 1, this was the IMF 1 (scale of 403m), whereas for transect 2, it was the medium scale of the IMF 2 (scale of 688m). For both transects, vegetation properties (vegetation cover and aboveground biomass) were the main factors affecting SOC distributions at their respective dominant scales. At each scale, the main effective factors could be identified although at the larger scales, their contributions to the overall variance were almost negligible. The distributions of SOC and the factors affecting it were found to be scale dependent. The results of this study highlighted the suitability of the MEMD method in revealing the main scale-specific factors that affect SOC distributions, which is necessary in understanding and managing this important soil property.

Discrimination of motor imagery tasks via information flow pattern of brain connectivity.

The effective connectivity refers explicitly to the influence that one neural system exerts over another in frequency domain. To investigate the propagation of neuronal activity in certain frequency can help us reveal the mechanisms of information processing by brain. This study investigates the detection of effective connectivity and analyzes the complex brain network connection mode associated with motor imagery (MI) tasks. The effective connectivity among the primary motor area is firstly explored using partial directed coherence (PDC) combined with multivariate empirical mode decomposition (MEMD) based on electroencephalography (EEG) data. Then a new approach is proposed to analyze the connection mode of the complex brain network via the information flow pattern. Our results demonstrate that significant effective connectivity exists in the bilateral hemisphere during the tasks, regardless of the left-/right-hand MI tasks. Furthermore, the out-in rate results of the information flow reveal the existence of the contralateral lateralization. The classification performance of left-/right-hand MI tasks can be improved by careful selection of intrinsic mode functions (IMFs). The proposed method can provide efficient features for the detection of MI tasks and has great potential to be applied in brain computer interface (BCI).