Singular Spectrum Analysis for Denoising Biomedical Signals

Biomedical signals such as electromyography (EMG), electrocardiography (ECG), and electroencephalography (EEG) are often contaminated by noise and physiological interference. In single-channel recordings, separation is particularly challenging when the signal and interference have overlapping spectral characteristics.

Singular Spectrum Analysis (SSA) has gained attention as a powerful non-parametric method for time-series decomposition and denoising. By transforming a one-dimensional signal into a trajectory matrix and applying Singular Value Decomposition (SVD), SSA enables separation of signal components based on their intrinsic structure. However, classical SSA relies on heuristic selection of singular values and is limited in handling non-stationary signals.

This work presents three main contributions to address these limitations. First, a Kurtosis-based Sliding SSA framework is developed for ECG interference removal from diaphragmatic EMG (EMGdi) by applying the SVD over a moving window, but at the cost of significantly increased computational complexity due to repeated SVD operations. Followed by an Updating Sliding SSA (USSSA) method using rank-1 SVD updates. USSSA achieves an approximately fivefold computational gain while maintaining reconstruction accuracy. Second, an Optimal Threshold SSA (OT-SSA) method is introduced, incorporating optimal singular value hard thresholding (SVHT) to provide automated singular-value selection and improved separation under non-Gaussian and coloured noise conditions. The proposed methods are evaluated using synthetic and real EMGdi and EEG signals, demonstrating effective ECG and EOG interference suppression while preserving the underlying signals.

Finally, OT-SSA is implemented on a low-cost ARM-based embedded system, achieving approximately 30 ms processing time and a measured system latency of approximately 125 ms for EMGdi signals using a $100\times50$ SVD window. These results demonstrate the feasibility of deploying the proposed SSA-based methods for real-time biomedical signal processing on resource-constrained embedded hardware.