# Research on a Noise Reduction Method Based on Multi-Resolution Singular Value Decomposition
## 1 Introduction  
Signals are inevitably subject to natural and man-made interference during acquisition and transmission. In high precision data analysis, even extremely weak noise interference can have a huge impact on the analysis results. Therefore, before signal processing it is necessary to first denoise it. Whether the noise can be removed from the disturbed observation signal is related not only to the nature of the interference and the form of the signal, but also to the manner in which the signal is processed. In practical applications, finding the best processing method to reduce noise aiming at different types of signal and interference has been a widely discussed problem in the field of signal processing. In recent decades, many signal denoising methods have been proposed, such as the empirical mode decomposition proposed by [PERSON] [1], the ensemble empirical mode decomposition, and the variational mode decomposition (VMD), etc. Among them, EMD has obvious advantages in dealingwith non-stationary and nonlinear data. It is suitable for analyzing nonlinear and non-stationary signal sequences and has good SNR. The key of this method is empirical mode decomposition, which can decompose complex signal into a finite number of intrinsic mode functions (IMFs) [2,3]. The decomposed IMF components contain local characteristic signal with different time scales of the original signal. However, EMD has non-negligible end-point effects and modal aliasing; EEMD [4] is a noise-assisted data analysis method proposed aiming at the deficiency of EMD. While using the noise-assisted signal to add the white noise background signal with a uniformly distribute, the signal regions with different scales will be automatically mapped to the appropriate scale related to the background white noise, which reduces the influence of the modal aliasing phenomenon, but the method has a large amount of computation, and the modal component is not controlled, it is easy to cause the function to not converge, which affects the accuracy of the algorithm [5]; VMD is to realize complex signal decomposition by finding the optimal solution of constrained variational model. Its essence is adaptive Wiener filtering [6], but the K value selection of variational mode decomposition will affect the decomposition result. In [7], a feature extraction method based on VMD and Hilbert transform is proposed. According to the power spectrum of PD signal, the double-threshold screening method is used to determine the number of decomposition modes in the VMD algorithm. Although the above several methods can realize the processing of noise signals, they all have the inevitable defects of modal aliasing. Singular value decomposition (SVD) is an orthogonal transformation that could transform the original matrix into a diagonal matrix whose eigenvalues reflect some of the main features of the original matrix. As a data processing method, SVD has been successfully applied to signal denoising processing and proved to be effective in avoiding modal aliasing. The main application of singular value decomposition in statistics is the principal component analysis (PCA), which can be used in pattern recognition [8, 9, 10, 11], data dimensionality reduction [12, 13], filter design [14, 15], denoising [16, 17], feature extraction and weak signal separation [18, 19, 20, 21, 22], face recognition [23, 24] and many other fields, and it has gained important applications. In10, the application of SVD in pattern recognition of partial discharge signals is studied.