A Comprehensive Review of Noise-Assisted Data Analysis Methods for Non-Linear and Non-Stationary Signals

Abstract

The processing and analysis of non-linear and non-stationary signals represent a persistent and critical challenge in modern signal processing. While traditional analytical techniques, such as the Fourier Transform, rely heavily on assumptions of linearity and stationarity, they often fail to capture localized transient phenomena. In response to these limitations, Empirical Mode Decomposition (EMD) and its subsequent noise-assisted variants—primarily Ensemble Empirical Mode Decomposition (EEMD) and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN)—have emerged as highly effective, fully data-driven alternatives. This paper presents an extensive review of noise-assisted data analysis methods spanning over two decades of research and literature. We deeply explore the theoretical foundations and mathematical models governing EMD, tracing the algorithmic evolution of noise-assisted variants designed specifically to combat the "mode mixing" problem. Furthermore, we systematically analyze the diverse applications of these methods across biomedical engineering, radar systems, geosciences, and image processing. By synthesizing 35 key academic publications, this review not only highlights the efficacy of these algorithms but also identifies critical research gaps. Specifically, we discuss the urgent need for optimizations enabling real-time processing, the lack of universal adaptive parameter selection frameworks, and the largely unexplored potential of integrating these decomposition techniques as front-end feature extractors for modern deep learning architectures. This comprehensive synthesis serves as a foundation for future innovations in non-stationary signal analysis.

Keywords