## 1 Introduction
### Relevant Works  
The background noise in PD detection mainly includes white noise and periodic narrowband noise [4]. Because the energy of white noise is evenly distributed at all frequencies, the wavelet coefficients of white noise decrease gradually with the increase in the wavelet decomposition scale, so the wavelet transform has a better removal effect on white noise [5,6]. In [7], a wavelet noise reduction method based on ant colony algorithm optimization is proposed. Using continuous derivative threshold function and Ant Colony Optimization (ACO), the global optimum threshold is found, and then the PD signal noise reduction is realized. However, the joint algorithm has obvious shortcomings in time and efficiency. In [8], adaptive dual-tree complex wavelet transform (ADTCWT) is used for PD signal noise reduction. The threshold value of the two-tree complex wavelet is determined by using the adaptive singular value decomposition method, and then the noise reduction is realized. However, the improved system still has oscillation error and will lose the edge of the signal [9]. Paper [9] proposed wavelet threshold and total variation theory for PD signal noise reduction. Through the combination of these two algorithms, the oscillation error can be reduced without the introduction of visible stair error. However, the selection of wavelet base function, wavelet threshold and decomposition level is largely dependent on human experience [10]. Paper [11] directly determines the decomposition layer for noise reduction through the spectral kurtosis diagram of the PD signal, thus avoiding the setting of the threshold coefficient, the parent wavelet and the number of decomposition layers. The results show that this method can remove white noise more effectively. In addition, the modal decomposition method has also received some attention in recent years due to its advantages of no preset basis function and strong adaptability. In [12], a PD signal noise reduction method based on new adaptive ensemble empirical mode decomposition (NAEEMD) is proposed. The noise reduction is accomplished by using a threshold criterion which combines the white Gaussian noise (WGN) spectrum and the mean cycle of energy density. However, the noise reduction method based on EMD or NAEEMD is often unable to eliminate the problem of modal aliasing and endpoint effect. In [13], S_VMD and Sdr_SampEn are used for PD signal noise reduction. The optimal modal parameter \(k\) of the VMD algorithm is determined by the Spearman correlation coefficient, and the noise reduction is completed by combining the spatial correlation recursive sample entropy criterion of each intrinsic mode function (IMF) and the wavelet threshold method. However, the Spearman coefficient can only ensure that the noisy PD signal is completely decomposed of the VMD algorithm, and the accurate extraction of PD signal characteristics in the decomposition process is not considered. Paper [14] proposed a noise reduction method to optimize MVMD parameters through image information entropy. Image information entropy is combined with the Pearson correlation coefficient to optimize MVMD modal parameter \(k\) to complete noise reduction. It can be seen that when \(k=8\), the PD signal has the greatest degree of certainty under this decomposition method, and its noise content is relatively small. However, a fixed empirical value is selected for the penalty factor, which is difficult to be universal for the decomposition of noisy PD signals. Moreover, when the content of narrowband interference in the signal is large, the noise reduction effect is not significant. Narrowband interference signals usually have specific frequency components and high power levels. When the frequency components of narrowband interference are similar to PD signals, EMD, MVMD and other methods may cause modal aliasing, which affects the accurate extraction of PD signals. Therefore, a separate narrowband interference signal filtering method is worth studying.