Key result
An efficient sliding Singular Spectrum Analysis algorithm evaluating rank-1 SVD updates in O(n^2) dramatically increases speed and effectively removes ECG from EMG signals.
Why the study?
Operating Singular Spectrum Analysis in a sliding manner carries a heavy computational cost due to the O(n^3) evaluation of full rank matrix SVD.
The proposed efficient sliding SSA algorithm significantly reduces computational cost from O(n³) to O(n²) for biomedical signal denoising, such as removing ECG artifacts from EMG signals.
May enable real-time EMG denoising clinically; leaves open prospective validation before routine use.
Previous work [1] has shown that Singular Spectrum Analysis (SSA) can be particularly effective at noise removal or signal separation in the case of single channel mixtures. The work presented here shows how the sliding or updating algorithm which performs best at signal separation can be implemented in a computationally efficient manner. The main computational burden involved in SSA is the evaluation of a full rank matrix Singular Value Decomposition (SVD). This process is well understood to be of O(n 3 ) where n is the rank of the matrix. Therefore, operation of the SSA algorithm in a sliding manner (once per new data sample) involves a very heavy computational cost. In this paper, we show it is possible to evaluate the rank-1 SVD update efficiently in O(n 2 ), thus dramatically increasing the speed of the sliding version of the SSA algorithm. Further, we demonstrate that our proposed sliding SSA can be particularly effective at removing ECG from EMG signals in an under-determined setting.
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Saeed et al. (2020) studied Biomedical signal denoising. Sliding Singular Spectrum Analysis (SSA) with rank-1 SVD update vs. Standard SSA algorithm was evaluated on Computational efficiency and signal separation effectiveness. An efficient sliding Singular Spectrum Analysis algorithm evaluating rank-1 SVD updates in O(n^2) dramatically increases speed and effectively removes ECG from EMG signals.
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