A general method for mode decomposition on additive mixture: Generalized Variational Mode Decomposition and its sequentialization

Abstract

Variational Mode Decomposition(VMD) method was proposed to separate non-stationary signal mixture by solving a optimization problem. This method is powerful and can reconstruct the signal components precisely when they are orthogonal(or quasi-orthogonal) in frequency domain. The crucial problem for VMD is that it requires the information of modal number before the decomposition. Also its applications are limited in 1D and 2D signal processing fields, of narrow scope.

In this paper, by inheriting and developing the core idea of VMD, we build a general form for this method and extend it to the modal decomposition for common additive mixture, not only limited in signal processing. To overcome the obstacle of modal number, we sequentialize the generalized VMD method, such that the modes can be extracted one by one, without knowing the modal number a priori. After the generalization and sequentialization for the VMD, we apply them in different fields of additive case, such as texture segmentation, Gaussian Mixture Model(GMM), clustering, etc. From the experiments, we conclude that the generalized and sequentialized VMD methods can solve variety classical problems from the view of modal decomposition, which implies that our methods have higher generality and wider applicability. A raw Matlab code for this algorithm is shown in https://github.com/changwangke/SGVMD_additive_Clustering/blob/main/SGVMD_clustering.m.