Efficient Algorithm to Implement Sliding Singular Spectrum Analysis with Application to Biomedical Signal Denoising

Abstract

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 $\mathcal{O}\left( {{n^3}} \right)$ 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 $\mathcal{O}\left( {{n^2}} \right)$, 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.