Multivariate group-sparse mode decomposition

Abstract

In signal decomposition, a complex and nonstationary signal is decomposed into a set of basic functions, usually called intrinsic mode functions (IMFs). In multivariate signal decomposition, it is assumed that analogous IMFs across all channels share common bandwidths (BWs). In this paper, a generic extension of the group-sparse mode decomposition (GSMD) for multivariate (multichannel) signal decomposition is developed. The univariate GSMD is based on the assumption that the spectral energy of the measured signal is concentrated in disjoint groups, and each group represents the spectral energy of one of the IMFs. This concept is generalized in the proposed algorithm to the multivariate measurements. Accordingly, the penalized least-squares objective function used for deriving GSMD is adapted in this paper to handle the multivariate measurements, where the weightedℓ0-norm is utilized as the penalty term, and the weighting parameters and the regularization parameter are calculated using techniques based on energy detection over short windows. In addition, two thresholding strategies were applied by the proposed algorithm to overcome the mode-mixing phenomenon. The derived algorithm is referred to as generalized GSMD (gGSMD). The gGSMD is further developed to handle the case when the analogous IMFs have disparate BWs across channels, and the resulting algorithm is referred to as multivariate GSMD (MvGSMD). The MvGSMD enjoys the following desired properties: robustness against noise, fast convergence, mode alignment, automatically estimating the number of IMFs, producing orthogonal IMFs, and efficiently adjusting the BW of each individual IMF even when analogous IMFs across channels have disparate BWs. All these properties were validated using numerical results on simulated data and real EEG and physiological data. The simulation results also show that the proposed algorithm outperforms many state-of-the-art multivariate signal decomposition algorithms.