Efficient and Adaptive Signal Denoising Based on Multistage Singular Spectrum Analysis

This article presents a multistage singular spectrum analysis (SSA) method to denoise a signal efficiently and adaptively. The multistage SSA is to apply the basic SSA recursively toward the noisy signal. Therefore, the noise-dominated components will be extracted out from the noisy signal stage by stage. However, the denoised signal is still noisy if the number of stages is small. On the other hand, after all the noise-dominated components have been extracted out by enough number of stages, some signal-dominated components begin to be moved into the noise group as the multistage SSA-based denoising proceeds. An adaptive criterion based on the correlation measure is proposed to terminate the multistage SSA-based denoising algorithm to prevent moving the signal-dominated components into the noise group. The multistage SSA-based denoising algorithm is efficient since the window length is selected as a small positive integer in every stage. Also, the adaptive stop criterion makes the proposed method avoid inappropriate parameter selection effectively. Computer numerical simulation results show that the proposed method has better denoising performance toward different test signals under different noise levels and needs less processing time when compared with the conventional SSA denoising method.