A novel algorithm for the decomposition of non-stationary multidimensional and multivariate signals

TL;DR

The paper addresses the challenge of decomposing nonstationary, high-dimensional signals that vary over space and time. It introduces MdMvFIF, a nonlinear, adaptive space-time extension of FIF that first extracts spatial IMFs and then temporal IMFs, using data-driven filter supports and FFT acceleration. The method is validated on synthetic examples and a global Earth temperature dataset, demonstrating effective separation of space and time frequency content and robustness to complex nonstationarities. This approach provides a versatile, efficient tool for multidimensional signal analysis with broad potential applications in geophysics and engineering.

Abstract

The decomposition of a signal is a fundamental tool in many fields of research, including signal processing, geophysics, astrophysics, engineering, medicine, and many more. By breaking down complex signals into simpler oscillatory components we can enhance the understanding and processing of the data, unveiling hidden information contained in them. Traditional methods, such as Fourier analysis and wavelet transforms, which are effective in handling mono-dimensional stationary signals struggle with non-stationary data sets and they require, this is the case of the wavelet, the selection of predefined basis functions. In contrast, the Empirical Mode Decomposition (EMD) method and its variants, such as Iterative Filtering (IF), have emerged as effective nonlinear approaches, adapting to signals without any need for a priori assumptions. To accelerate these methods, the Fast Iterative Filtering (FIF) algorithm was developed, and further extensions, such as Multivariate FIF (MvFIF) and Multidimensional FIF (FIF2), have been proposed to handle higher-dimensional data. In this work, we introduce the Multidimensional and Multivariate Fast Iterative Filtering (MdMvFIF) technique, an innovative method that extends FIF to handle data that vary simultaneously in space and time. This new algorithm is capable of extracting Intrinsic Mode Functions (IMFs) from complex signals that vary in both space and time, overcoming limitations found in prior methods. The potentiality of the proposed method is demonstrated through applications to artificial and real-life signals, highlighting its versatility and effectiveness in decomposing multidimensional and multivariate nonstationary signals. The MdMvFIF method offers a powerful tool for advanced signal analysis across many scientific and engineering disciplines.

Figures (13)

• Figure 1: Example 1. Left panel: Signal at time $t=0$. Right panel: Time evolution for position $\mathbf{v}=(150,\,150)$.
• Figure 2: Example 1. Left panel: 3D signal evolution in the second space variable and time. Right panel: 3D signal evolution in space at different time stamps.
• Figure 3: Example 1. Left panel: time decomposition for data at position $\mathbf{v}=(100,\,10)$. Right panel: time decomposition for data at position $\mathbf{v}=(150,\,150)$.
• Figure 4: Example 1. From left to right, first, second IMF and trend over space.
• Figure 5: Example 1. Differences between the ground truth and the first, and second IMF and trend produced over space by MdMvFIF algorithm, respectively.