A Modified Multivariate Variational Mode Decomposition for Multi-channel Signal Processing

The multivariate variational mode decomposition (MVMD) is an optimization-based method that allows simultaneous processing of non-stationary multi-channel signals. It has recently garnered considerable attention due to its excellent signal separation capability and robustness against the sampling frequency. Nevertheless, MVMD also encounters certain challenges. Specifically, in cases where the signal is significantly disturbed by noise, MVMD struggles to accurately decompose the correct sub-signals. Moreover, the computational time required for MVMD increases dramatically with the number of channels, thereby making it challenging to solve multivariate signals with high-density channel. An effective solution to these issues is the implementation of the proposed modified MVMD (MMVMD) technique. This method aims to convert the task of finding multiple multivariate oscillations corresponding to MVMD into finding multiple univariate oscillations in one-dimensional space. The satisfactory noise robustness and faster decomposition rate of MMVMD, especially for signals with a large number of channels, are demonstrated by its application on multivariate synthetic signals. We finally provide further convincing validation of the effectiveness of the algorithm through the analysis of a 4-channel EEG signal.