Filter Bank Property of Multivariate Empirical Mode Decomposition
TL;DR: It is found that, similarly to EMD, MEMD also essentially acts as a dyadic filter bank on each channel of the multivariate input signal, but better aligns the corresponding intrinsic mode functions from different channels across the same frequency range which is crucial for real world applications.
Abstract: The multivariate empirical mode decomposition (MEMD) algorithm has been recently proposed in order to make empirical mode decomposition (EMD) suitable for processing of multichannel signals. To shed further light on its performance, we analyze the behavior of MEMD in the presence of white Gaussian noise. It is found that, similarly to EMD, MEMD also essentially acts as a dyadic filter bank on each channel of the multivariate input signal. However, unlike EMD, MEMD better aligns the corresponding intrinsic mode functions (IMFs) from different channels across the same frequency range which is crucial for real world applications. A noise-assisted MEMD (N-A MEMD) method is next proposed to help resolve the mode mixing problem in the existing EMD algorithms. Simulations on both synthetic signals and on artifact removal from real world electroencephalogram (EEG) support the analysis.
Citations
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TL;DR: Simulations using real-world case studies illuminate several practical aspects, such as the role of noise in T-F localization, dealing with unbalanced multichannel data, and nonuniform sampling for computational efficiency.
Abstract: This article addresses data-driven time-frequency (T-F) analysis of multivariate signals, which is achieved through the empirical mode decomposition (EMD) algorithm and its noise assisted and multivariate extensions, the ensemble EMD (EEMD) and multivariate EMD (MEMD). Unlike standard approaches that project data onto predefined basis functions (harmonic, wavelet) thus coloring the representation and blurring the interpretation, the bases for EMD are derived from the data and can be nonlinear and nonstationary. For multivariate data, we show how the MEMD aligns intrinsic joint rotational modes across the intermittent, drifting, and noisy data channels, facilitating advanced synchrony and data fusion analyses. Simulations using real-world case studies illuminate several practical aspects, such as the role of noise in T-F localization, dealing with unbalanced multichannel data, and nonuniform sampling for computational efficiency.
359 citations
Cites background from "Filter Bank Property of Multivariat..."
...This property also explains enhanced T-F localization of noise-aided EMD algorithms [15], [31]....
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...IEEE SIGNAL PROCESSING MAGAZINE [80] NOvEMbER 2013 n -dimensional signal subspace and an adjacent subspace of l-independent WGN realizations [31]....
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TL;DR: This study proves that the time complexity of the EMD/EEMD is actually equivalent to that of the Fourier Transform.
Abstract: It has been claimed that the empirical mode decomposition (EMD) and its improved version the ensemble EMD (EEMD) are computation intensive. In this study we will prove that the time complexity of the EMD/EEMD, which has never been analyzed before, is actually equivalent to that of the Fourier Transform. Numerical examples are presented to verify that EMD/EEMD is, in fact, a computationally efficient method.
324 citations
Cites methods from "Filter Bank Property of Multivariat..."
...To overcome this problem, the EEMD algorithm [2] and the noise-assisted MEMD [3] have been proposed....
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01 Jan 2013
TL;DR: It is shown that direct multichannel processing via MEMD allows for enhanced localization of the frequency information in EEG, and, in particular, its noise-assisted mode of operation (NA-MEMD) provides a highly localized time-frequency representation.
Abstract: Brain electrical activity recorded via electroencephalogram (EEG) is the most convenient means for brain-computer interface (BCI), and is notoriously noisy. The information of interest is located in well defined frequency bands, and a number of standard frequency estimation algorithms have been used for feature extraction. To deal with data nonstationarity, low signal-to-noise ratio, and closely spaced frequency bands of interest, we investigate the effectiveness of recently introduced multivariate extensions of empirical mode decomposition (MEMD) in motor imagery BCI. We show that direct multichannel processing via MEMD allows for enhanced localization of the frequency information in EEG, and, in particular, its noise-assisted mode of operation (NA-MEMD) provides a highly localized time-frequency representation. Comparative analysis with other state of the art methods on both synthetic benchmark examples and a well established BCI motor imagery dataset support the analysis.
208 citations
Cites background from "Filter Bank Property of Multivariat..."
...A plot of the amplitude versus time and instantaneous frequency , that is, amplitude contours on the time-frequency plane, is called the Hilbert–Huang spectrogram (HHS), , and represents a time-frequency spectrogram of a nonlinear and nonstationary signal....
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TL;DR: A MEMD-based feature extraction method is proposed to process multichannel EEG signals for emotion recognition and the results are compared with similar previous studies for benchmarking.
Abstract: 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.
192 citations
Cites background or methods from "Filter Bank Property of Multivariat..."
...2 Multivariate empirical mode decomposition filter bank structure [25]...
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...Finally, MEMD algorithm is suggested to generalize EMD algorithm for multivariate data with up to 32 channels, and filter bank properties of the EMD algorithms have been also investigated [5, 14, 25]....
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TL;DR: Two techniques of decomposition of the ECG signal into suitable bases of functions are proposed, such as the empirical mode decomposition (EMD) and the wavelet analysis, and performance achieved by applying these algorithms to extract the respiratory waveform shape from single-channel ECG is presented.
Abstract: The respiratory signal can be accurately evaluated by single-channel electrocardiogram (ECG) processing, as shown in recent literature. Indirect methods to derive the respiratory signal from ECG can benefit from a simultaneous study of both respiratory and cardiac activities. These methods lead to major advantages such as low cost, high efficiency, and continuous noninvasive respiratory monitoring. The aim of this paper is to reconstruct the waveform of the respiratory signal by processing single-channel ECG. To achieve these goals, two techniques of decomposition of the ECG signal into suitable bases of functions are proposed, such as the empirical mode decomposition (EMD) and the wavelet analysis. The results highlight the main differences between them in terms of both theoretical foundations, and performance achieved by applying these algorithms to extract the respiratory waveform shape from single-channel ECG are presented. The results also show that both algorithms are able to reconstruct the respiratory waveform, although the EMD is able to break down the original signal without a preselected basis function, as it is necessary for wavelet decomposition. The EMD outperforms the wavelet approach. Some results on experimental data are presented.
177 citations
Cites methods from "Filter Bank Property of Multivariat..."
...A possible way to solve this problem is to consider a novel algorithm referred to as Noise-Assisted Multivariate Empirical Mode Decomposition, which is based on MEMD but which is also able to exploit the filter bank properties of MEMD [28]....
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...Decomposition, which is based on MEMD but which is also able to exploit the filter bank properties of MEMD [28]....
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...Fig 5 illustrates the results achieved by applying NoiseAssisted MEMD to the same ECG used in Fig....
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...However, recently, a multivariate version of the EMD (MEMD) has been successfully proposed [21]....
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References
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TL;DR: In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.
Abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...
18,956 citations
TL;DR: The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF.
Abstract: A new Ensemble Empirical Mode Decomposition (EEMD) is presented. This new approach consists of sifting an ensemble of white noise-added signal (data) and treats the mean as the final true result. Finite, not infinitesimal, amplitude white noise is necessary to force the ensemble to exhaust all possible solutions in the sifting process, thus making the different scale signals to collate in the proper intrinsic mode functions (IMF) dictated by the dyadic filter banks. As EEMD is a time–space analysis method, the added white noise is averaged out with sufficient number of trials; the only persistent part that survives the averaging process is the component of the signal (original data), which is then treated as the true and more physical meaningful answer. The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF. With this ensemble mean, one can separate scales naturall...
6,437 citations
"Filter Bank Property of Multivariat..." refers methods in this paper
...Both these criteria have been used in the simulations presented in this work....
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TL;DR: It turns out that EMD acts essentially as a dyadic filter bank resembling those involved in wavelet decompositions, and the hierarchy of the extracted modes may be similarly exploited for getting access to the Hurst exponent.
Abstract: Empirical mode decomposition (EMD) has recently been pioneered by Huang et al. for adaptively representing nonstationary signals as sums of zero-mean amplitude modulation frequency modulation components. In order to better understand the way EMD behaves in stochastic situations involving broadband noise, we report here on numerical experiments based on fractional Gaussian noise. In such a case, it turns out that EMD acts essentially as a dyadic filter bank resembling those involved in wavelet decompositions. It is also pointed out that the hierarchy of the extracted modes may be similarly exploited for getting access to the Hurst exponent.
2,304 citations
"Filter Bank Property of Multivariat..." refers methods in this paper
...5: For a set of direction vectors, calculate the mean of the envelope curves as (1) 1The Matlab code for multivariate EMD along with some synthetic and real world multivariate signals are available from http://www.commsp.ee.ic.ac.uk/ ~mandic/research/emd.htm....
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TL;DR: In this article, empirical experiments on white noise using the empirical mode decomposition (EMD) method were conducted and it was shown empirically that the EMD is effectively a dyadic filter, the intrinsic mode function (IMF) components are all normally distributed, and the Fourier spectra of the IMF components cover the same area on a semi-logarithmic period scale.
Abstract: Based on numerical experiments on white noise using the empirical mode decomposition (EMD) method, we find empirically that the EMD is effectively a dyadic filter, the intrinsic mode function (IMF) components are all normally distributed, and the Fourier spectra of the IMF components are all identical and cover the same area on a semi–logarithmic period scale. Expanding from these empirical findings, we further deduce that the product of the energy density of IMF and its corresponding averaged period is a constant, and that the energy–density function is chi–squared distributed. Furthermore, we derive the energy–density spread function of the IMF components. Through these results, we establish a method of assigning statistical significance of information content for IMF components from any noisy data. Southern Oscillation Index data are used to illustrate the methodology developed here.
1,573 citations
"Filter Bank Property of Multivariat..." refers methods in this paper
...5: For a set of direction vectors, calculate the mean of the envelope curves as (1) 1The Matlab code for multivariate EMD along with some synthetic and real world multivariate signals are available from http://www.commsp.ee.ic.ac.uk/ ~mandic/research/emd.htm....
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TL;DR: Hilbert-Huang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research.
Abstract: [1] Data analysis has been one of the core activities in scientific research, but limited by the availability of analysis methods in the past, data analysis was often relegated to data processing. To accommodate the variety of data generated by nonlinear and nonstationary processes in nature, the analysis method would have to be adaptive. Hilbert-Huang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research. In this review, we will briefly introduce the method, list some recent developments, demonstrate the usefulness of the method, summarize some applications in various geophysical research areas, and finally, discuss the outstanding open problems. We hope this review will serve as an introduction of the method for those new to the concepts, as well as a summary of the present frontiers of its applications for experienced research scientists.
1,533 citations
"Filter Bank Property of Multivariat..." refers methods in this paper
...In order to obtain projections of the input signal in n-dimensional spaces, the sampling scheme based on low discrepancy Hammersley sequence was used in [9]....
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