Multi-Channel Neighborhood-Constrained Variational Mode Decomposition

Abstract

In many multi-channel engineering problems, the information relevant to the task is concentrated in one channel, while the other information plays an auxiliary role. In forecasting, the quantity to be predicted is the primary source of information and the covariates support it; in image processing, the image itself is primary and contextual data are auxiliary. This paper introduces multi-channel neighborhood-constrained variational mode decomposition (NCVMD), an extension of variational mode decomposition (VMD) built on this hierarchy. Where multivariate VMD (MVMD) aligns the modes’ central frequencies symmetrically and exactly across all channels, NCVMD distinguishes a main channel from auxiliary ones and makes the degree of alignment tunable, reallocating the decomposition error away from the priority channel by a controllable amount. A second contribution is a formal analysis of the resulting optimization problem, which delimits what can be asserted and what cannot. Every subproblem of the alternating scheme is convex and admits a unique closed-form solution, and the main channel provably attains the unconstrained VMD optimum, which MVMD cannot. The joint problem, however, remains nonconvex, so global optimality is not guaranteed. Experiments on synthetic and real-world data confirm the predicted behaviour.