Multivariate Empirical Mode Decomposition Research Articles

Application of Multivariate EMD to Improve Quality VLF-EM Data: Synthetic and Fields Data

A method for enhancing VLF˗EM data based on Multivariate Empirical Mode Decomposition (EMD) was presented. The noise assisted multivariate empirical mode decomposition (NA-MEMD) approach to simultaneously decompose bivariate data.The NA-MEMD is applied to enhance bivariate VLF˗EM data. The method was also tested on a synthetic and two fields VLF-EM data sets. The results indicate that the filtered VLF˗EM data based on the NA-MEMD results better data and easier to interpret or further analyzed. In addition, the 2D resistivity profile result estimated from the inversion of filtered VLF˗EM data is appropriate to geological condition.

The Removal of EOG Artifacts From EEG Signals Using Independent Component Analysis and Multivariate Empirical Mode Decomposition.

The recorded electroencephalography (EEG) signals are usually contaminated by electrooculography (EOG) artifacts. In this paper, by using independent component analysis (ICA) and multivariate empirical mode decomposition (MEMD), the ICA-based MEMD method was proposed to remove EOG artifacts (EOAs) from multichannel EEG signals. First, the EEG signals were decomposed by the MEMD into multiple multivariate intrinsic mode functions (MIMFs). The EOG-related components were then extracted by reconstructing the MIMFs corresponding to EOAs. After performing the ICA of EOG-related signals, the EOG-linked independent components were distinguished and rejected. Finally, the clean EEG signals were reconstructed by implementing the inverse transform of ICA and MEMD. The results of simulated and real data suggested that the proposed method could successfully eliminate EOAs from EEG signals and preserve useful EEG information with little loss. By comparing with other existing techniques, the proposed method achieved much improvement in terms of the increase of signal-to-noise and the decrease of mean square error after removing EOAs.

Time-Frequency Analysis of Nonstationary Process Based on Multivariate Empirical Mode Decomposition

Currently, empirical mode decomposition (EMD) has become a popular data-driven time-frequency analysis method for nonstationary and nonlinear data. However, it is still limited to univariate data due to the number and/or scale misalignment for multivariate data. A newly developed multivariate EMD (MEMD) scheme decomposes multivariate data simultaneously and thus leads to mode alignment and minimizes mode mixing. In addition, an improved amplitude and frequency modulation (AM-FM) decomposition algorithm presented here provides an estimation of a more meaningful instantaneous amplitude and frequency than the widely used Hilbert transform (HT). Both of these facilitate development of a time-frequency analysis framework for multivariate nonstationary and nonlinear data analysis. In this paper, MEMD-based scalogram and coscalogram, and instantaneous frequency spectra and cospectra are proposed to characterize a multivariate nonstationary process. The scalogram and instantaneous frequency spectra capture spectral evolution of each component while the coscalogram and instantaneous frequency cospectra reveal embedded intermittent correlation between two components. Compared with scale-based scalogram and coscalogram, frequency-based instantaneous frequency spectra and cospectra provide a more detailed portrait of multivariate data. The effectiveness of the proposed MEMD-based time-frequency analysis framework is demonstrated by numerical examples of a thunderstorm downburst and an earthquake ground motion. Also, the results from the MEMD-based approach are compared with those based on a continuous wavelet transform, which further reinforces the effectiveness of the proposed framework.

Stability monitor for Boiling Water Reactors based on the Multivariate Empirical Mode Decomposition

In this work a stability monitor based on a novel technique is presented. This monitor permits to launch general alarms indicating incipient high decay ratios (DR) and out-of-phase oscillations, in a simultaneous way time along. The implemented methodology to determine the estimations of DR and out-of-phase oscillations is based on the Multivariate Empirical Mode Decomposition (MEMD) processing the information obtained from all LPRMs located across the core of Boiling Water Reactor (BWR). The extracted modes with the MEMD, called the Intrinsic Mode Functions (IMFs), permit to tracking the oscillation associated to the density wave. The Case 9 (presenting high DRs and apparently out-of-phase oscillations simultaneously) from the Ringhals stability benchmark was used to show the effectiveness of the proposed methodology.

Multivariate Empirical Mode Decomposition Derived Multi‐Scale Spatial Relationships between Saturated Hydraulic Conductivity and Basic Soil Properties

Saturated hydraulic conductivity (Ks) is affected by various factors operating at different scales. This study identified the multi‐scale spatial relationships between Ks and selected basic soil properties (soil organic matter [SOM], clay, silt, and sand contents, and bulk density) along two landscape transects (with various soil textures and land use covers) on the Loess Plateau. Multivariate empirical mode decomposition (MEMD) yielded four different intrinsic mode functions (IMFs) for the multivariate data series of each transect according to the scale of occurrence. The dominant scales in terms of explained variance of Ks were IMF1 (scale: 403 m) for transect 1, and IMF1 and IMF2 (scale: 407 and 775 m) for transect 2. The multi‐scale correlation between Ks and soil properties was more complex for transect 1 due to a more fragmented landscape. For each IMF or residue, Ks was predicted using the identified factors that significantly affected it at that IMF scale or residue. The summation of the four predicted IMFs and the residue predicted Ks at the measurement scale, and was more accurate than predictions based on simple multiple linear regressions between Ks and the other soil properties. Soil particle size components were the main contributors in explaining Ks variability for both landscape transects, mostly due to their contributions from IMF1; however, SOM was also a major contributor for transect 2, mainly due to contributions from IMF2. Using MEMD has great potential in characterizing scale‐dependent spatial relationships between soil properties in complicated landscape ecosystems.

Multi-scale pixel-based image fusion using multivariate empirical mode decomposition.

A novel scheme to perform the fusion of multiple images using the multivariate empirical mode decomposition (MEMD) algorithm is proposed. Standard multi-scale fusion techniques make a priori assumptions regarding input data, whereas standard univariate empirical mode decomposition (EMD)-based fusion techniques suffer from inherent mode mixing and mode misalignment issues, characterized respectively by either a single intrinsic mode function (IMF) containing multiple scales or the same indexed IMFs corresponding to multiple input images carrying different frequency information. We show that MEMD overcomes these problems by being fully data adaptive and by aligning common frequency scales from multiple channels, thus enabling their comparison at a pixel level and subsequent fusion at multiple data scales. We then demonstrate the potential of the proposed scheme on a large dataset of real-world multi-exposure and multi-focus images and compare the results against those obtained from standard fusion algorithms, including the principal component analysis (PCA), discrete wavelet transform (DWT) and non-subsampled contourlet transform (NCT). A variety of image fusion quality measures are employed for the objective evaluation of the proposed method. We also report the results of a hypothesis testing approach on our large image dataset to identify statistically-significant performance differences.

Time-Frequency Analysis of Electrohysterogram for Classification of Term and Preterm Birth

In this paper, a novel method for the classification of term and preterm birth is proposed based on time-frequency analysis of electrohysterogram (EHG) using multivariate empirical mode decomposition (MEMD). EHG is a promising study for preterm birth prediction, because it is lowcost and accurate compared to other preterm birth prediction methods, such as tocodynamometry (TOCO). Previous studies on preterm birth prediction applied prefilterings based on Fourier analysis of an EHG, followed by feature extraction and classification, even though Fourier analysis is suboptimal to biomedical signals, such as EHG, because of its nonlinearity and nonstationarity. Therefore, the proposed method applies prefiltering based on MEMD instead of Fourier-based prefilters before extracting the sample entropy feature and classifying the term and preterm birth groups. For the evaluation, the Physionet term-preterm EHG database was used where the proposed method and Fourier prefiltering-based method were adopted for comparative study. The result showed that the area under curve (AUC) of the receiver operating characteristic (ROC) was increased by 0.0351 when MEMD was used instead of the Fourier-based prefilter.

Epileptic Seizures Detection based on Empirical Mode Decomposition and Hilbert-Huang transform of EEG Signal

The electrical activities of brain fluctuate frequently and can be analyzed using electroencephalogram (EEG) signals. We present a new method for classification of ictal and seizure-free intracranial EEG recordings. The proposed method uses the application of multivariate empirical mode decomposition (MEMD) algorithm combines with the Hilbert transform as the Hilbert-Huang transform (HHT) and analyzing spectral energy of the intrinsic mode function of the signal. EMD uses the characteristics of signals to adaptively decompose them to several intrinsic mode functions (IMFs). Hilbert transforms (HTs) are then used to transform the IMFs into instantaneous frequencies (IFs), to obtain the signals time-frequency-energy distributions. Classification of the EEG signal that is epileptic seizure exists or not has been done using support vector machine. The algorithm was tested in 6 intracranial channels EEG records acquired in 9 patients with refractory epilepsy and validated by the Epilepsy Center of the University Hospital of Freiburg. The experimental results show that the proposed method efficiently detects the presence of epileptic seizure in EEG signals and also showed a reasonable accuracy in detection.

Causal inference in neuronal time-series using adaptive decomposition

BackgroundThe assessment of directed functional connectivity from neuronal data is increasingly common in neuroscience by applying measures based in the Granger causality (GC) framework. Although initially these consisted in simple analyses based on directionality strengths, current methods aim to discriminate causal effects both in time and frequency domain. New methodWe study the effect of adaptive data analysis on the GC framework by combining empirical mode decomposition (EMD) and causal analysis of neuronal signals. EMD decomposes data into simple amplitude and phase modulated oscillatory modes, the intrinsic mode functions (IMFs), from which it is possible to compute their instantaneous frequencies (IFs). Hence, we propose a method where causality is estimated between IMFs with comparable IFs, in a static or time-varying procedure, and then attributed to the frequencies corresponding to the IF of the driving IMF for improved frequency localization. ResultsWe apply a thorough simulation framework involving all possible combinations of EMD algorithms with causality metrics and realistically simulated datasets. Results show that synchrosqueezing wavelet transform and noise-assisted multivariate EMD, paired with generalized partial directed coherence or with Geweke's GC, provide the highest sensitivity and specificity results. Comparison with existing methodsCompared to standard causal analysis, the output of selected representative instances of this methodology result in the fulfillment of performance criteria in a well-known benchmark with real animal epicranial recordings and improved frequency resolution for simulated neural data. ConclusionsThis study presents empirical evidence that adaptive data analysis is a fruitful addition to the existing causal framework.

Multivariate empirical mode decomposition based sub-frequency bands analysis of the default mode network: a resting-state fMRI data study

Abstract Resting-state functional connectivity reveals intrinsic, spontaneous networks that elucidate the functional architecture of the human brain. The default mode network (DMN) is the most important and stable intrinsic connectivity network (ICN), which involves several cognition functions, such as episodic memory and self-introspection. It has been suggested that low-frequency fluctuations in the blood oxygenation level-dependent (BOLD) signal during rest reflect the neuronal baseline activity of the brain and these low-frequency fluctuations correspond to functionally relevant resting-state networks. Several studies have revealed that the function of the brain is accomplished in certain low sub-frequency band. However, the concerned frequency bands are determined by experience, neglecting the intrinsic information of BOLD time series. In this study, we apply a full data-driven analysis, i.e., multivariate empirical mode decomposition (MEMD), to decompose resting-state fMRI data into the different sub-band DMNs, aiming to reveal the corresponding connectivity functions in separate sub-band DMN. Our results revealed that MEMD can adaptively decompose signals into intrinsic mode functions (IMFs) with the similar patterns across subjects. Furthermore, the sub-network constructed from the IMFs revealed that the different sub-band DMNs correspond to the different brain functional connectivity, inferring the possible relationships between sub-frequency band and cognitions. Owing to its data-driven merit, the proposed MEMD analysis may provide a new insight for fMRI-related studies.

Simple tai chi exercise for improving elderly postural stability via complexity index analysis

The main purpose of this study is to investigate twice a day simple 9-step tai chi effects of the center of pressure (COP) and physiological signals of elderly people. Data are collected from the COP signals, electromyography (EMG), and pulse oximetry for 1 min for the period of 12 weeks. The COP signals are analyzed using multivariate empirical mode decomposition and multivariate multiscale entropy to work out and compare the complexity index (CI). Subjects in this experiment are over 65 years old who are divided into 11 men and 7 women; the average age is 74 ± 8.18 years. In conclusion, it is found that tai chi exercise can improve human body balance by just walking some simple steps in our experiment. However, we cannot find any effect or improvement in the pulse oximetry and EMG signals analysis.

Time-variant coherence between heart rate variability and EEG activity in epileptic patients: an advanced coupling analysis between physiological networks

Time-variant coherence analysis between the heart rate variability (HRV) and the channel-related envelopes of adaptively selected EEG components was used as an indicator for the occurrence of (correlative) couplings between the central autonomic network (CAN) and the epileptic network before, during and after epileptic seizures. Two groups of patients were investigated, a group with left and a group with right hemispheric temporal lobe epilepsy. The individual EEG components were extracted by a signal-adaptive approach, the multivariate empirical mode decomposition, and the envelopes of each resulting intrinsic mode function (IMF) were computed by using Hilbert transform. Two IMFs, whose envelopes were strongly correlated with the HRV’s low-frequency oscillation (HRV-LF; ≈0.1 Hz) before and after the seizure were identified. The frequency ranges of these IMFs correspond to the EEG delta-band. The time-variant coherence was statistically quantified and tensor decomposition of the time-frequency coherence maps was applied to explore the topography-time-frequency characteristics of the coherence analysis. Results allow the hypothesis that couplings between the CAN, which controls the cardiovascular-cardiorespiratory system, and the ‘epileptic neural network’ exist. Additionally, our results confirm the hypothesis of a right hemispheric lateralization of sympathetic cardiac control of the HRV-LF.

Two-dimensional nonlinear geophysical data filtering using the multidimensional EEMD method

A variety of two-dimensional (2D) empirical mode decomposition (EMD) methods have been proposed in the last decade. Furthermore, the multidimensional EMD algorithm and its parallel class, multivariate EMD (MEMD), are available in recent years. From those achievements, it is possible to design an efficient 2D nonlinear filter for geophysical data processing. We introduce a robust 2D nonlinear filter which can be applied to enhance the signal of 2D geophysical data or to highlight the feature component on an image. We did this by replacing the conventionally used smooth interpolation in the ensemble empirical mode decomposition (EEMD) algorithm with a piecewise interpolation method. The one-dimensional (1D) EEMD procedures were consecutively performed in all directions, and then the comparable minimal scale combination technique was applied to the decomposed components. The theoretical derivation, model simulation, and real data applications are demonstrated in this paper. The proposed filtering method is effective in improving the image resolution by suppressing the random noise added in the simulation example and strong low frequency track corrugation noise bands with background noise in the field example. Furthermore, the algorithm can be easily extended to higher dimensions by repeating the same procedure in the succeeding dimension. To evaluate the proposed method, one data set is processed separately by using the enhanced analytic signal method and the multivariate EMD (MEMD) algorithm, and the results from these two methods are compared with that of the proposed method. A general equation for generating three-dimensional (3D) EEMD components based on the comparable minimal scale combination principle is derived for further applications.

Multivariate Empirical Mode Decomposition applied to the estimation of the decay ratio and out-of-phase oscillations in BWRs

This work presents a novel method based on the Multivariate Empirical Mode Decomposition (MEMD) to estimate the Decay Ratio (DR) and the apparition of a possible out-of-phase oscillation in Boiling Water Reactors (BWRs). The MEMD algorithm, have the potential to find common oscillatory modes within multivariate data called Intrisic Mode Functions (IMF). Based on this fact, we implement the MEMD technique to find the common oscillatory mode (density wave) in BWRs considering the measurements obtained in each Local Power Range Monitor (LPRM) through the entire core. These IMFs, analyzed simultaneously in time, permit to obtain an estimation of the DR and; also give some considerations about an incipient out-of-phase oscillation through the phase measured between two specific LPRMs. Effectiveness of the proposed method is demonstrated on a specific challenging case from the Forsmark stability benchmark.

Characterizing scale specific depth persistence of soil water content along two landscape transects

• MEMD identified dominant scales of spatial SWC variation along two transects. • Dominant spatial variation scales were at 376 and 677 m; and at 639 and 1304 m. • Depth persistence of SWC was scale dependent and strongest at the dominant scales. • Higher degrees of landscape fragmentation resulted in weaker depth persistence. • During recharge periods, weaker depth persistence occurred in the fragmented transect. Information on depth persistence of soil water content ( SWC ) is useful for adopting data assimilation techniques in integrating remote sensing data and soil water modeling. The objective of this study was to investigate the scale- and season-specific depth persistence of 0–1.0 m SWC distribution in two transects (having different soils and plant cover) in a watershed on the Chinese Loess Plateau, by combining multivariate empirical mode decomposition (MEMD) with Spearman’s rank correlation analysis. Three or four intrinsic mode functions (IMFs) representing specific scales were separated out for SWC of each soil layer. The dominant scales in terms of explaining the spatial variance of SWC for Transect 1 were about 376 m (IMF1) and 677 m (IMF2), and those for Transect 2 were about 639 m (IMF2) and 1304 m (IMF3). Depth persistence of SWC varied with scale, and was the strongest at the dominant scales. The multi-scale depth persistence was weaker along Transect 1 than along Transect 2 due to the higher degree of landscape fragmentation resulting from greater human activity along Transect 1. Weaker depth persistence at each scale was mainly observed at wet conditions for Transect 1. Strong season-related depth persistence was also mainly observed at the dominant scales for both transects. The results of this study are useful for developing sampling strategies for soil water measurements, since information about depth persistence reduces the efforts involved in measuring SWC in deeper layers.

The VLF-EM imaging of potential collapse on the LUSI embankment

Abstract Collapse and overtopping repeatedly occur in LUSI Embankment. Discontinuities (crack or fracture) in the embankment are major reasons for embankment failures or collapses. Very-low frequency electromagnetic (VLF-EM) measurement is essentially a non-destructive technique which displays subsurface 2-D cross section of resistivity. The cross section result has the possibility of detecting discontinuities and liquid saturation in embankment before it collapsed by observing which part of it in the cross section has low resistivity. This paper presents results of a survey conducted at the LUSI embankment in Eastern Java, Indonesia in a part of potential collapse. VLF-EM profiles measured along the embankment crest provided an overview of the whole embankment and served to detect anomalous zones. The noise assisted multivariate empirical mode decomposition (NA-MEMD) is applied to reject unwanted VLF-EM noise and Inv2DVLF software is applied to obtain result of 2-D resistivity models. In the selected area, the drill log and the standard penetration test (SPT) value gave detailed information about subsurface layer below embankment. This information is valuable for supporting 2-D resistivity image obtained from VLF-EM data inversion. Furthermore, the low resistivity in embankment layer is associated to discontinuities (fracture, crack or fault) along the embankment which caused its collapse.

Using Empirical Mode Decomposition with Spatio-Temporal dynamics to classify single-trial Motor Imagery in BCI.

This paper introduces a new signal processing method called Spatio-Temporal Multivariate Empirical Mode Decomposition (ST-MEMD). It is a new variation of Empirical Mode Decomposition (EMD) that takes spatial and temporal information into account simultaneously rather than processing each signal source in isolation. The original and new methods were tested on single-trial electroencephalogram data with a two-class problem, in this case data using the Motor Imagery paradigm in brain-computer interfacing. However, whilst ST-MEMD retained the increase in sensitivity and specificity from adding spatial data, the new temporal data made no meaningful difference in terms of performance.

EEG gamma band oscillations differentiate the planning of spatially directed movements of the arm versus eye: multivariate empirical mode decomposition analysis.

The neural dynamics underlying the coordination of spatially-directed limb and eye movements in humans is not well understood. Part of the difficulty has been a lack of signal processing tools suitable for the analysis of nonstationary electroencephalographic (EEG) signals. Here, we use multivariate empirical mode decomposition (MEMD), a data-driven approach that does not employ predefined basis functions. High-density EEG, and arm and eye movements were synchronously recorded in 10 subjects performing time-constrained reaching and/or eye movements. Subjects were allowed to move both the hand and the eyes, only the hand, or only the eyes following a 500-700 ms delay interval where the hand and gaze remained on a central fixation cross. An additional condition involved a nonspatially-directed "lift" movement of the hand. The neural activity during a 500 ms delay interval was decomposed into intrinsic mode functions (IMFs) using MEMD. Classification analysis revealed that gamma band (30 Hz) IMFs produced more classifiable features differentiating the EEG according to the different upcoming movements. A benchmark test using conventional algorithms demonstrated that MEMD was the best algorithm for extracting oscillatory bands from EEG, yielding the best classification of the different movement conditions. The gamma rhythm decomposed using MEMD showed a higher correlation with the eventual movement accuracy than any other band rhythm and than any other algorithm.

Search for information-bearing components in neural data.

Multivariate empirical mode decomposition (MEMD) is an important extension of EMD, suitable for processing multichannel data. It can adaptively decompose multivariate data into a set of intrinsic mode functions (IMFs) that are matched both in number and in frequency scale. This method is thus holds great potential for the analysis of multi- channel neural recordings as it is capable of ensuring all the intrinsic oscillatory modes are aligned not only across channels, but also across trials. Given a plethora of IMFs derived by MEMD, a question of significant interest is how to identify which IMFs contain information, and which IMFs are noise. Existing methods that exploit the dyadic filter bank structure of white noise decomposition are insufficient since the IMFs do not always adhere to the presumed dyadic relationship. Here we propose a statistical procedure to identify information-bearing IMFs, which is built upon MEMD that allows adding noise as separate channels to serve as a reference to facilitate IMF identification. In this procedure, Wasserstein distance is used to measure the similarity between the reference IMF and that from data. Simulations are performed to validate the method. Local field potentials from cortex of monkeys while performing visual tasks are used for demonstration.

EEG classification in a single-trial basis for vowel speech perception using multivariate empirical mode decomposition

Objective. The objective of this study is to find components that might be related to phoneme representation in the brain and to discriminate EEG responses for each speech sound on a trial basis. Approach. We used multivariate empirical mode decomposition (MEMD) and common spatial pattern for feature extraction. We chose three vowel stimuli, /a/, /i/ and /u/, based on previous findings, such that the brain can detect change in formant frequency (F2) of vowels. EEG activity was recorded from seven native Korean speakers at Gwangju Institute of Science and Technology. We applied MEMD over EEG channels to extract speech-related brain signal sources, and looked for the intrinsic mode functions which were dominant in the alpha bands. After the MEMD procedure, we applied the common spatial pattern algorithm for enhancing the classification performance, and used linear discriminant analysis (LDA) as a classifier. Main results. The brain responses to the three vowels could be classified as one of the learned phonemes on a single-trial basis with our approach. Significance. The results of our study show that brain responses to vowels can be classified for single trials using MEMD and LDA. This approach may not only become a useful tool for the brain–computer interface but it could also be used for discriminating the neural correlates of categorical speech perception.