A different view on the vector-valued empirical mode decomposition (VEMD)
This work addresses the problem of extending EMD to vector-valued signals, offering an alternative to multivariate EMD for multi-scale time-frequency analysis.
The paper proposes a vector-valued empirical mode decomposition (VEMD) that uses a novel back projection method to interpolate vector-valued envelopes from 1-D envelopes in projected space, outperforming state-of-the-art methods in numerical simulations for 4-D signals.
The empirical mode decomposition (EMD) has achieved its reputation by providing a multi-scale time-frequency representation of nonlinear and/or nonstationary signals. To extend this method to vector-valued signals (VvS) in multidimensional (multi-D) space, a multivariate EMD (MEMD) has been designed recently, which employs an ensemble projection to extract local extremum locations (LELs) of the given VvS with respect to different projection directions. This idea successfully overcomes the problems of locally defining extrema of VvS. Different from the MEMD, where vector-valued envelopes (VvEs) are interpolated based on LELs extracted from the 1-D projected signal, the vector-valued EMD (VEMD) proposed in this paper employs a novel back projection method to interpolate the VvEs from 1-D envelopes in the projected space. Considering typical 4-D coordinates (3-D location and time), we show by numerical simulations that the VEMD outperforms state-of-art methods.