Singular spectral analysis‐based denoising without computing singular values via augmented Lagrange multiplier algorithm

Abstract

This study proposes an augmented Lagrange multiplier-based method to perform the singular spectral analysis-based denoising without computing the singular values. In particular, the one-dimensional (1D) signal is first mapped to a trajectory matrix using the window length L . Second, the trajectory matrix is represented as the sum of the signal dominant matrix and the noise-dominant matrix. The determination of these two matrices is formulated as an optimisation problem with the objective function being the sum of the rank of the signal dominant matrix and the norm of the noise-dominant matrix. This study employs the Schatten q-norm operator with and the double nuclear-norm penalty for approximating the rank operator as well as the minimum concave penalty (MCP)-norm operator for approximating the -norm operator. Third, some auxiliary variables are introduced and the augmented Lagrange multiplier algorithm is applied to find the optimal solution. Finally, the 1D denoised signal is obtained by applying the diagonal averaging method to the obtained signal dominant matrix. Computer numerical simulation results show that the authors' proposed method outperforms the existing methods.