Optimal Threshold Singular Spectrum Analysis for Efficient Electrocardiogram Interference Removal

Singular Spectrum Analysis (SSA) has become well known for its ability to effectively separate mixtures of signals with overlapping spectral content but with different statistical natures. In this paper, we show how a new approach to grouping the singular values that efficiently denoise biomedical signals, specifically, mixtures of Electrocardiogram and Electromyogram signals. It is based on optimal Singular Value Hard Thresholding (SVHT) but for signals that are periodic or quasi-periodic in nature. An optimal thresholding technique can provide similar results with much smaller trajectory matrices and thus significantly reduced computational burden. The resultant Singular Value Decomposition process is significantly faster and shows similar performance to kurtosis based sliding SSA with a reduction in computational complexity of the order of 12,500 times. This technique is well suited to real-time implementation for de-noising biomedical signals on the fly.