# Research on a Noise Reduction Method Based on Multi-Resolution Singular Value Decomposition
## 1 Introduction
The singular value power percentage is defined as the eigenvector of the partial discharge signal, and it is verified that the discharge signal eigenvalue vector constructed with the singular value power percentage can reflect the original signal characteristics; In [17], the order of the effective rank is determined by the fast Fourier transform of the noise signal, and the reconstruction matrix is determined for SVD decomposition to reduce the noise of the Gaussian white noise-contaminated signal, the output SNR is improved. In [21], at the basis of SVD, the singular value decomposition based on slip matrix sequence is proposed, and the difference spectrum, main singular sum, maximum eigenvalue reconstruction and optimal filter design are introduced to realize the fault feature extraction of rolling bearings under noise background. The above results obtained by the SVD method for noise reduction are essentially the same level of spatial and identical resolution results, and cannot reveal the signal profile and detail features at different levels. Drawing on the idea of wavelet multi-resolution analysis, [PERSON] [25] proposed a new research idea, using the recursive idea to construct the signal into a second-order matrix, and perform singular value decomposition on the matrix layer by layer to obtain the decomposition results of signals in different levels of space and different resolutions, so as to achieve multi-resolution decomposition similar to wavelet analysis that can decompose signals into a series of different hierarchical subspaces. This is essentially different from previous SVD-based signal processing methods, called MRSVD. [PERSON] [26] proposed a method based on generalized morphological filtering and multi-resolution singular value decomposition. The signal is denoised by MRSVD and the kurtosis criterion is used to select the most detailed fault signal for Hilbert envelope spectrum analyze to obtain the characteristic information of the fault signal. [PERSON] [27] decomposed the noise image into four different frequency bands by multi-resolution singular value decomposition, reconstructs the separated high-frequency detailed sub-bands to obtain the noise image, and selects the appropriate threshold to remove the noise signal. The signal noise reduction mentioned in the above several documents does not involve the analysis of the noise reduction effect, and does not consider the factors affecting the noise reduction effect. Based on the theory of MRSVD, this paper studies the noise reduction model of multi-division structure MRSVD and summarizes it. The SNR and MSE are used as evaluation indexes to verify the several noise reduction models, and the MRSVD is obtained under different conditions and then comparing MRSVD with traditional noise reduction methods, the results show that the MRSVD method avoids defects such as EMD and EEMD to a certain extent, and also has better adaptability and robustness. The results show that the MRSVD method avoids EMD to a certain extent. Defects such as EEMD have the advantages of better adaptability and robustness, and have certain research value in the application of noise reduction. Specifically, the organizational structure of this paper is as follows: Section 2 briefly introduces the methods, including MRSVD and multi-division structure MRSVD, and introduces the noise reduction model and evaluation indicators; Section 3 conducts simulation analysis and case verification, and analyzes and discusses the results. The conclusions are given in Section 4.