# A New Adaptive Spatial Filtering Method in the Wavelet Domain for Medical Images
## 3 Results and Discussions
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{**Soft Truncation**} & \multicolumn{3}{c}{**Soft Truncation with**} & \multicolumn{3}{c}{**Soft Truncation with**} & \multicolumn{3}{c}{**Soft Truncation with**} & \multicolumn{3}{c}{**Soft Truncation with**} & \multicolumn{3}{c}{**Soft Truncation with**} \\
**Image** & \(\sigma\) & \multicolumn{3}{c}{**Initial**} & \multicolumn{3}{c}{**with Optimal**} & \multicolumn{3}{c}{**Local Statistics = 3**} & \multicolumn{3}{c}{**Local Statistics = 3**} & \multicolumn{3}{c}{**Local Statistics = 3**} & \multicolumn{3}{c}{**Local Statistics = 4**} & \multicolumn{3}{c}{**Local Statistics = 4**} \\  & & & \multicolumn{3}{c}{**Threshold Values**} & \multicolumn{3}{c}{**L = 3**} & \multicolumn{3}{c}{**L = 5**} & \multicolumn{3}{c}{**L = 7**} & \multicolumn{3}{c}{**L = 3**} & \multicolumn{3}{c}{**L = 5**} \\ \cline{2-15}  & & \multicolumn{3}{c}{**PSNR**} & \multicolumn{3}{c}{**C (\%)**} & \multicolumn{3}{c}{**PSNR**} & \multicolumn{3}{c}{**PSNR**} & \multicolumn{3}{c}{**C (\%)**} & \multicolumn{3}{c}{**PSNR**} & \multicolumn{3}{c}{**C (\%)**} & \multicolumn{3}{c}{**PSNR**} & \multicolumn{3}{c}{**PSNR**} \\  & & & \multicolumn{3}{c}{**(dB)**} & \multicolumn{3}{c}{**(dB)**} & \multicolumn{3}{c}{**(dB)**} & \multicolumn{3}{c}{**(dB)**} & \multicolumn{3}{c}{**(dB)**} & \multicolumn{3}{c}{**(dB)**} & \multicolumn{3}{c}{**(dB)**} & \multicolumn{3}{c}{**(dB)**} & \multicolumn{3}{c}{**(dB)**} & \multicolumn{3}{c}{**(dB)**} & \multicolumn{3}{c}{**(dB)**} \\ \hline \multirow{2}{*}{_Loss_} & 0.05 & 26.00 & 63.94 & 29.74 & 61.96 & 30.27 & 65.84 & 30.18 & 65.51 & 30.08 & 65.75 & 30.27 & 65.67 & 30.18 & 65.48 \\ \cline{2-15}  & 0.1 & 20.06 & 48.10 & 26.13 & 44.65 & 26.59 & 46.74 & 26.57 & 45.66 & 26.49 & 46.38 & 26.01 & 46.78 & 26.59 & 45.80 \\ \cline{2-15}  & 0.05 & 26.09 & 63.59 & 27.49 & 62.67 & 27.65 & 62.56 & 27.65 & 62.74 & 27.65 & 62.76 & 62.36 & 27.65 & 62.86 \\ \cline{2-15}  & 0.1 & 20.13 & 48.07 & 23.38 & 44.76 & 23.45 & 43.75 & 23.48 & 44.03 & 23.49 & 43.87 & 23.45 & 43.99 & 23.48 & 43.96 \\ \hline \multirow{2}{*}{_Hease_} & 0.05 & 26.05 & 65.47 & 31.17 & 62.89 & 31.72 & 66.93 & 31.57 & 66.59 & 31.42 & 66.93 & 31.73 & 67.03 & 31.58 & 66.51 \\ \cline{2-15}  & 0.1 & 20.18 & 49.04 & 27.56 & 51.59 & 28.07 & 53.78 & 27.98 & 52.55 & 27.80 & 52.66 & 28.12 & 53.78 & 28.02 & 52.81 \\ \hline \multirow{2}{*}{_Soft_} & 0.05 & 26.03 & 64.03 & 30.44 & 62.72 & 30.87 & 65.06 & 30.74 & 64.75 & 30.66 & 65.22 & 30.87 & 65.00 & 30.75 & 64.92 \\ \cline{2-15}  & 0.1 & 20.03 & 47.09 & 26.83 & 46.12 & 27.10 & 49.53 & 27.08 & 48.16 & 27.00 & 47.75 & 27.14 & 49.92 & 27.11 & 49.22 \\ \hline \multirow{2}{*}{_Propers_} & 0.05 & 26.04 & 63.50 & 30.08 & 60.78 & 30.44 & 62.36 & 30.32 & 63.44 & 30.22 & 63.36 & 30.43 & 62.40 & 30.32 & 63.40 \\ \cline{2-15}  & 0.1 & 20.16 & 50.88 & 26.51 & 48.65 & 26.78 & 49.28 & 26.73 & 49.28 & 26.66 & 48.47 & 26.79 & 49.30 & 26.74 & 49.12 \\ \hline \end{tabular}
\end{table} 
Table 3: Dependence of the results obtained in the first stage of the proposed algorithm, as a function of Table 2 (L + 1). In all cases, better results are obtained when using local statistics compared to optimal threshold, for both PSNR and C (improvement of the contours). The proposed algorithm was tested on different images with dimensions of \(256\times 256\) pixels and \(512\times 512\) pixels, under white Gaussian additive dispersion noise degradation conditions: \(\sigma~{}=~{}0.05\) and \(\sigma~{}=~{}0.1\). The results are presented in Figure 4.  
The analysis of the data presented in the Appendix A shows that the effect of the threshold value used to obtain the contour map from the hierarchical correlation map does not depend on the processed image (as in the case of optimal threshold values in the case of soft truncation), but only on dispersion of the disturbing noise. Thus, for a noise dispersion \(\sigma~{}=~{}0.05\), the optimal value is between \(0.1\) and \(0.15\), and for \(\sigma~{}=~{}0.1\), between \(0.15\) and \(0.175\).