A different view on the vector-valued empirical mode decomposition (VEMD)

TL;DR

This paper introduces a novel vector-valued empirical mode decomposition (VEMD) method that uses back projection for envelope interpolation, outperforming existing methods in analyzing multidimensional signals.

Contribution

The paper proposes a new VEMD approach employing back projection, offering improved performance over traditional MEMD in multidimensional signal analysis.

Findings

VEMD outperforms state-of-the-art methods in numerical simulations.

The back projection approach effectively interpolates vector-valued envelopes.

VEMD provides better multi-scale time-frequency analysis for 4-D signals.

Abstract

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.