# Research on a Noise Reduction Method Based on Multi-Resolution Singular Value Decomposition
## 3 Analysis
### The Optimal Model of MRSVD
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**MSE**} & \multicolumn{5}{c}{\(x1\)} & \multicolumn{5}{c}{\(x2\)} \\ \cline{2-9}  & \(-\)**5** & **1** & **5** & **20** & \(-\)**5** & **1** & **5** & **20** \\ \hline Undecomposed & **3.141** & **0.777** & **0.352** & **0.009** & **3.308** & **0.827** & **0.286** & **0.013** \\ Two-division & 0.184 & 0.071 & 0.022 & 0.002 & 0.138 & 0.112 & 0.039 & 0.004 \\ Three-division(N = 1) & 0.389 & 0.247 & 0.156 & 0.138 & 0.399 & 0.365 & 0.291 & 0.244 \\ Three-division(N = 2) & 0.552 & 0.266 & 0.183 & 0.118 & 0.518 & 0.369 & 0.272 & 0.234 \\ Four-division(N = 1) & 0.199 & 0.087 & 0.033 & \(1.9\times 10^{-3}\) & 0.182 & 0.129 & 0.059 & 0.010 \\ Four-division(N = 2) & 0.186 & 0.073 & 0.023 & \(6\times 10^{-4}\) & 0.154 & 0.113 & 0.039 & \(1.9\times 10^{-3}\) \\ Four-division(N = 3) & 0.265 & 0.124 & 0.036 & \(9.4\times 10^{-4}\) & 0.291 & 0.117 & 0.047 & \(2.1\times 10^{-3}\) \\ \hline \hline \end{tabular}  
The value of the bold mark indicates the MSE before the decomposition.  
\end{table} 
Table 2: The MSE of different noise reduction models. \begin{table} \begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Decomposition Layer**} & \multicolumn{5}{c}{\(x1\)} & \multicolumn{5}{c}{\(x2\)} \\ \cline{2-7}  & \(-\)**5** & **1** & **5** & **20** & \(-\)**5** & **1** & **5** & **20** \\ \hline Two-division & 78 & 48 & 29 & 7 & 22 & 9 & 8 & 1 \\ Three-division(N = 1) & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ Three-division(N = 2) & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ Four-division(N = 1) & 18 & 9 & 1 & 1 & 4 & 1 & 1 & 1 \\ Four-division(N = 2) & 5734 & 4144 & 2583 & 1755 & 251 & 139 & 90 & 15 \\ Four-division(N = 3) & 5623 & 4994 & 3673 & 3112 & 366 & 185 & 88 & 25 \\ \hline \hline \end{tabular}   
By observing Tables 1–3, it is usually satisfied (\(-5\) db, \(1\) db, \(5\) db) that:  
Maximum value of SNR: two-division \(>\) four-division \(>\) three-division  
Minimum value of MSE: two-division \(<\) four-division \(<\) three-division  
When the noise power is much smaller than the original signal (\(20\) db), the following is satisfied:  
Maximum value of SNR: four-division (N = \(2\)) \(>\) two-division \(>\) three-division  
Minimum value of MSE: four-division (N = \(2\)) \(<\) two-division \(<\) three-division  
The noise reduction effect of the three-division method is inferior to the two-division method and the four-division method, because the power leakage of the three-division method is more serious when it is decomposed. In fact, when the number of division of decomposition method is even, the effect is always better than that is odd. The SNR of the four-division method is slightly higher than the two  
there are requirements for noise reduction efficiency. Considering the actual situation, the accuracy cannot be simply pursued, and the noise reduction speed must also be considered. The two-division method can achieve booth higher precision and speed in most cases, so it can be considered that the two-division method is the optimal noise reduction model in MRSVD.