The sparse and low-rank interpretation of SVD-based denoising for vibration signals

Vibration signal denoising is one of the most important steps in condition monitoring and fault diagnosis, and SVD-based methods are a vital part of advanced signal denoising due to their non-parametric and simple properties. The relation-ships between SVD-based denoising and other advanced signal processing methods are very significant and can help speed up the development of SVD-based denoising methods. There is limited prior work into the sparse and low-rank meaning of SVD-based denoising. In this paper, we build the relationships among SVD-based denoising, sparse l₀-norm minimization, sparse weighted l₁-norm minimization, and weighted low-rank models, when the dictionary is designed by left and right singular matrices in sparse minimization. Using the derived conclusion, we establish weighted soft singular value decomposition (WSSVD) for vibration signal denoising. Finally, we perform one experimental study to verify the effectiveness of WSSVD considering impulse interference and amplitude fidelity.