Deep LSTM Surrogates for MEMD: A Noise-Assisted Approach to EEG Intrinsic Mode Function Extraction

In this paper, we propose a deep learning-based surrogate model for Multivariate Empirical Mode Decomposition (MEMD) using Long Short-Term Memory (LSTM) networks, aimed at efficiently extracting Intrinsic Mode Functions (IMFs) from electroencephalographic (EEG) signals. Unlike traditional data-driven methods, our approach leverages temporal sequence modeling to learn the decomposition process in an end-to-end fashion. We further enhance the decomposition targets by employing Noise-Assisted MEMD (NA-MEMD), which stabilizes mode separation and mitigates mode mixing effects, leading to better supervised learning signals. Extensive experiments on synthetic and real EEG data demonstrate the superior performance of the proposed LSTM surrogate over conventional feedforward neural networks and standard MEMD-based targets. Specifically, the LSTM trained on NA-MEMD outputs achieved the lowest mean squared error (MSE) and the highest signal-to-noise ratio (SNR), significantly outperforming the feedforward baseline, even when compared using the Power Spectral Density (PSD). These results confirm the effectiveness of combining LSTM architectures with noise-assisted decomposition strategies to approximate nonlinear signal analysis tasks such as MEMD. The proposed surrogate model offers a fast and accurate alternative to classical empirical methods, enabling real-time and scalable EEG analysis.