Multi-Channel Neighborhood-Constrained Variational Mode Decomposition

Authors:
  • GTGiuseppe La Tona
    Giuseppe La Tona
  • MDMatteo Diez
    Matteo Diez
  • MMMarco Montuori
    Marco Montuori
  • MPMaria Carmela Di Piazza
    Maria Carmela Di Piazza
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Abstract
This paper introduces Multi-Channel Neighborhood-Constrained Variational Mode Decomposition (NCVMD), a novel extension of Variational Mode Decomposition (VMD). When working with multi-channel signals, aligning mode frequencies serves as a criterion for grouping modes with similar frequencies and enabling mode-level processing. This requirement must be achieved while maintaining an acceptable error in the decomposition, and has been investigated by an approach called Multivariate Variational Mode Decomposition (MVMD), which forces a perfect alignment of the channels' modes' central frequencies at the expense of the decomposition error. Our approach differs in two key ways: first, by making a hierarchical distinction in a multi-channel signal between a primary (main) channel and others that provide auxiliary information; and second, by allowing tunable alignment between channel decomposition. Both these aspects reduce the decomposition error in the main channel at the expense of the auxiliary channels, at a customizable degree. These distinctive features make the method particularly well-suited for applications such as weighted image fusion, signal denoising, and time series forecasting; in these domains, there are clear advantages to both establishing a hierarchical processing framework for the signal's channels and operating at mode level, where intrinsic oscillatory patterns can be extracted and processed independently. We demonstrate the effectiveness of NCVMD through experiments on both synthetic and real-world datasets. The results indicate that NCVMD preserves a pure VMD-based decomposition for the main channel, maintains acceptable decomposition errors for the auxiliary channels, and achieves a high degree of mode frequency alignment across channels.
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