# 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} \hline \hline \multirow{2}{*}{**Image**} & \multirow{2}{*}{**Initial Values**} & \multirow{2}{*}{**Processing Stage**} & \multicolumn{3}{c}{**Number of Wavelet**} & \multicolumn{2}{c}{**Number of Wavelet**} \\  & & & \multicolumn{2}{c}{**Decomposition Levels \(N=3\)**} & \multicolumn{2}{c}{**Decomposition Levels \(N=4\)**} \\ \cline{5-8}  & & & **PSNR (dB)** & **C (\%)** & **PSNR (dB)** & **C (\%)** \\ \hline \multirow{8}{*}{_Lenu_} & \(\sigma\ =\ 0.05\) & After the second stage & 30.27 & 65.84 & 30.27 & 65.67 \\  & _PSNR_ = 26.00 dB & Using the correlation map & 30.19 & 66.09 & 30.19 & 66.31 \\  & C = 65.84\% & Filtered correlation map & 30.22 & 65.98 & 30.23 & **66.23** \\ \cline{2-8}  & \(\sigma\ =\ 0.05\) & After the second stage & 26.59 & 46.74 & 26.61 & 46.78 \\  & _PSNR_ = 26.00 dB & Using the correlation map & 26.29 & 48.17 & 26.30 & 47.99 \\  & C = 65.84\% & Filtered correlation map & 26.50 & 48.20 & 26.53 & **48.55** \\ \hline \multirow{8}{*}{_Bridge_} & \(\sigma\ =\ 0.05\) & After the second stage & 27.59 & 61.26 & 27.59 & 61.15 \\  & _PSNR_ = 26.03 dB & Using the correlation map & 27.54 & 62.83 & 27.53 & 62.96 \\  & C = 62.96\% & Filtered correlation map & 27.56 & 62.49 & 27.55 & **62.53** \\ \cline{2-8}  & \(\sigma\ =\ 0.1\) & After the second stage & 23.48 & 44.66 & 23.49 & 44.81 \\  & _PSNR_ = 20.19 dB & Using the correlation map & 23.38 & 44.82 & 23.38 & 44.97 \\  & C = 47.44\% & Filtered correlation map & 23.46 & 44.49 & 23.47 & **44.76** \\ \hline \multirow{8}{*}{_Aerial_} & \(\sigma\ =\ 0.05\) & After the second stage & 28.15 & 68.36 & 28.15 & 68.39 \\  & _PSNR_ = 26.06 dB & Using the correlation map & 28.10 & 69.55 & 28.10 & 69.37 \\  & C = 70.14\% & Filtered correlation map & 28.13 & **69.39** & 28.12 & 69.29 \\ \cline{2-8}  & \(\sigma\ =\ 0.1\) & After the second stage & 24.21 & 49.91 & 24.21 & 49.86 \\ \cline{2-8}  & _PSNR_ = 20.15 dB & Using the correlation map & 24.07 & 52.75 & 24.06 & 53.13 \\  & C = 54.39\% & Filtered correlation map & 24.17 & 52.02 & 24.16 & **52.68** \\ \hline \multirow{8}{*}{_Bart_} & \(\sigma\ =\ 0.05\) & After the second stage & 30.88 & 64.61 & 30.89 & 64.64 \\  & _PSNR_ = 26.03 dB & Using the correlation map & 30.80 & 65.22 & 30.81 & 65.24 \\ \cline{1-1}  & C = 64.53\% & Filtered correlation map & 30.84 & 64.75 & 30.85 & **64.92** \\ \cline{1-1} \cline{2-8}  & \(\sigma\ =\ 0.1\) & After the second stage & 27.07 & 47.54 & 27.09 & 47.58 \\ \cline{1-1}  & _PSNR_ = 20.07 dB & Using the correlation map & 26.72 & 48.84 & 26.72 & 49.43 \\ \cline{1-1}  & C = 47.50\% & Filtered correlation map & 26.96 & 48.16 & 26.99 & **48.76** \\ \hline \multirow{8}{*}{_House_} & \(\sigma\ =\ 0.05\) & After the second stage & 31.71 & 65.99 & 31.71 & 69.91 \\ \cline{1-1}  & _PSNR_ = 26.05 dB & Using the correlation map & 31.64 & 67.16 & 31.67 & 67.24 \\ \cline{1-1}  & C = 63.96\% & Filtered correlation map & 31.67 & 66.82 & 31.70 & **66.95** \\ \cline{1-1} \cline{2-8}  & \(\sigma\ =\ 0.1\) & After the second stage & 28.03 & 53.28 & 28.07 & 53.26 \\ \cline{1-1}  & _PSNR_ = 20.10 dB & Using the correlation map & 27.66 & 53.85 & 27.69 & 54.32 \\ \cline{1-1}  & C = 49.66\% & Filtered correlation map & 27.98 & 53.26 & 28.05 & **53.49** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Dependence of the results obtained by applying the filtering algorithm proposed, depending on the number of wavelet decomposition levels. The test images were \(256\times 256\) pixels and were degraded with white Gaussian additive noise. The threshold values used to obtain the contour map from the hierarchical correlation map are \(\text{t}_{\text{c}}\ =\ 0.1\) for \(\sigma\ =\ 0.05\) and \(\text{t}_{\text{c}}\ =\ 0.15\) for \(\sigma\ =\ 0.1\). It is also found that variant A leads to better overall results than in variant B, but the calculation effort is higher in this case.