Optimal and Bidirectional optimal Empirical Mode Decomposition

Abstract

The empirical mode decomposition (EMD) was recently proposed as a new time-frequency analysis tool for nonstationary and nonlinear signals. Although the EMD is able to find the intrinsic modes of the signal and is completely self-adaptive, it does not have any implication on optimality. In some situation, when certain optimality is considered, we need a more flexible signal decomposition and reconstruction scheme. We propose a modified version ofthe EMD, which enhances the capability of the EMD. The proposed modified EMD algorithm gives the best estimate to a given signal in the minimum mean square error sense. Two different formulations are proposed. The first one utilizes a linear weighting for the intrinsic mode functions (IMF). The second algorithm adopts a bidirectional weighting, namely, it not only uses weighting for IMF modes, but also exploits the correlations between samples in a specific window and carries out filtering in the window. These two new EMD methods extend the capability of the traditional EMD and is well suited for optimal signal recovery. Simulation studies are performed to show the application of the proposed optimal EMD algorithms to denoising problem.

Classification of Motor Imagery BCI Using Multivariate Empirical Mode Decomposition

“…Analysis of the motor imagery response in Section IV-B illustrates the high level of accuracy that is achievable using MEMD/NA-MEMD for time-frequency analysis. While the SST gave a similar performance, it inherited the problems of high frequency resolution associated with wavelets and was not sensitive to frequency components above 20 Hz, critically ignoring the full range of the beta band (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30). In addition to the spectrogram analysis, the accurate estimation of synthetic and rhythms using NA-MEMD in the time domain was also investigated.…”

“…7 have been shown to include some parts of the band (20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30). However, the classification results obtained using IMF were always outperformed by features that included IMF and only.…”

Time-Frequency Analysis of EEG Asymmetry Using Bivariate Empirical Mode Decomposition

“…These results illustrate that the enhanced BEMD performance is caused by more accurate component estimation and not by virtue of better sifting. 1 For more detail on the combination of EMD and Wiener filter we refer to [24]. It can therefore be deduced that mutual information between the real and the imaginary parts of the BEMD allowed for a more accurate estimate of the common components at the IMF level.…”

Derivative-optimized empirical mode decomposition for the Hilbert–Huang transform

“…For instance, the signal is approximately represented by a linear combination of original IMFs with weighting parameters, which are determined using the least square error relative to the original signal. This algorithm is called optimal EMD (OEMD) for one-dimensional weights and bidirectional optimal EMD (BOEMD) for twodimensional weight matrix so as to facilitate approximation by window-based filtering [6]. However, OEMD and BOEMD are limited by their block-based nature, and use of adaptive filters was proposed [7].…”