# Research on a Noise Reduction Method Based on Multi-Resolution Singular Value Decomposition
## 3 Analysis
### Comparison among Multiple Models  
In order to test the noise reduction effect of MRSVD (The two-division method), this paper selects EMD, EEMD, VMD, SVD, wavelet decomposition and the two-division method for comparative analysis. Among them, EMD, EEMD, and VMD decompose the signal into multi-order intrinsic mode function (IMF) in the case of selecting optimal parameters, and the components with severe modal aliasing are discarded and reconstruct the remain component; Wavelet decomposition is to select the db3 wavelet as the wave obtained by decomposing and reconstructing the fundamental wave; SVD is to reconstruct the signal by making the order of the effective rank to be twice the number of signal center frequency. The wave obtained by the above several noise reduction models are all obtained under the optimal parameters, and the wave decomposed by MRSVD are also the results obtained by selecting the number of optimal decomposition layer based on the optimal model. Figures 6 and 7 show the noise reduction results of two experimental signals at 1 db using several models. As shown these figures, the black curve shows the waveform of the original signal. It can be seen that the waveforms of EMD, EEMD, VMD, SVD and wavelet decomposition differ from the original signal under different signals. For signal \(x1\), the deviation between the waveform of EMD and VMD and the original signal is the largest, and the deviation between the waveform of SVD and MRSVD is smaller comparing with the original signal. For signal \(x2\), the deviation of the EMD and wavelet decomposition waveform from the original signal is the largest, the waveforms of SVD and MRSVD have less deviation from the original signal. In general, these noise reduction models have their own advantages, but only MRSVD has the highest coincidence with the original signal. Moreover  
It can be seen from Tables 4 and 5 that when the noise power is large, EMD, EEMD, VMD, and wavelet decomposition are obviously not as good as the MRSVD for the improvement of the SNR. For signal \(x2\), the noise reduction effect of EMD is not even better than before at 20 db, although the SNR of EEMD is slightly higher than MRSVD in this case, the MSE is still large overall. In most cases, MRSVD has a higher SNR, and MRSVD has a smaller MSE than other methods. This shows that the MRSVD has a good noise reduction effect and a more stable performance. In order to more intuitively see the decomposition effects of several models under different noise powers, the trends of the SNR and the MSE of several models under different noise powers are made for the experimental signals \(x1\) and \(x2\), respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**SNR/db**} & \multicolumn{4}{c}{\(x1\)} & \multicolumn{4}{c}{\(x2\)} \\ \cline{2-9}  & \(-5\) **db** & \(1\) **db** & \(5\) **db** & \(20\) **db** & \(-5\) **db** & \(1\) **db** & \(5\) **db** & \(20\) **db** \\ \hline EMD & 1.786 & 7.273 & 10.376 & 26.005 & \(-0.258\) & 2.957 & 5.078 & 6.329 \\ EEMD & 1.850 & 8.380 & 12.854 & 26.642 & 1.745 & 8.555 & 12.305 & 27.652 \\ VMD & 0.206 & 6.004 & 9.542 & 25.472 & 4.533 & 10.477 & 13.146 & 20.405 \\ SVD & 8.946 & 11.842 & 13.346 & 26.685 & 6.759 & 11.031 & 14.186 & 24.919 \\ MRSVD & 9.182 & 12.621 & 14.210 & 26.718 & 7.129 & 12.526 & 15.618 & 26.458 \\ Wavelet decomposition & 6.191 & 5.928 & 6.266 & 7.005 & 4.078 & 4.784 & 5.033 & 5.134 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: SNR of various noise reduction models at different noise powers.