Robust and Efficient Harmonics Denoising in Large Dataset Based on Random SVD and Soft Thresholding

The Hankel matrix of harmonic signals has the important low-rank property, based on which the principal components (or the eigenvectors) extracted from the matrix by singular value decomposition (SVD) could be applied for harmonic signal denoising. However, SVD is time-consuming, and may even fail to converge when the data matrix is too large. To overcome the computational difficulties of SVD for the big dataset, dimension reduction of the matrix is necessary, but it results in a significant reduction on signal intensities. In this paper, we proposed an efficient and robust denoising method for harmonic signals with large data. First, the Hankel matrix of the harmonic signal is constructed and randomly projected onto a lower dimensional subspace with a Gaussian matrix. Second, SVD on the matrix with reduced dimension is performed to extract essential eigenvectors, applying which a smooth signal with simplified compositions is reconstructed from the original noisy signal. Third, the threshold of signal to noise is analyzed on the smooth signal, then a soft thresholding algorithm is performed to obtain a denoised result from the original noisy signal. The simulation and experimental results have proved the robustness and effectiveness of this method.