# A New Adaptive Spatial Filtering Method in the Wavelet Domain for Medical Images
## 3 Results and Discussions  
Table 2 compares the results obtained in the case of processing the details sub bands corresponding to the first scale of a wavelet transformation by the method described by [PERSON] and [PERSON] (2007) (adaptive soft truncation with contextual modeling), which was presented in the previous paragraph, and applying the first step of the proposed method. As it can be seen from the data presented in Table 3, even in the case of applying only the first two steps of the proposed algorithm, better results are obtained both in terms of PSNR and in terms of contour conservation, given by the C coefficient. This coefficient is computed based on the reduction factor and represents how much of the contours were preserved from the original image. Regarding the proposed method, it can be found that, as the window size increases, the results are weaker both in terms of PSNR and in terms of the \(C\) coefficient. This can be justified by the fact that those signal-induced wavelet coefficients are grouped, and  
It can be observed that in all the considered cases, better results are obtained in _PSNR_ terms than in the case of soft truncation with optimal threshold values, in many cases obtaining even higher \(C\) coefficients than the initial ones, hence an improvement of the contours. Considering an ideal contour map, determined based on the image which is not degraded with noise, the simulations show (Appendix A) that, by the proposed method, an improvement of the contours can be obtained, expressed by higher values of the \(C\) coefficient, in the conditions in which the noise reduction is not affected, which is expressed by constant _PSNR_ values. In the real case, only the noise-degraded image is available, the contour map being determined based on it. As it can be seen in Figure 3, false contour points appear in this case, resulting in a smaller amount of noise removed. Therefore, on the hierarchical correlation map, before determining the contours, we proceed to process it with a median-hybrid filter, described in [72; 73; 74]. As it can be seen in Figure 3 and from the data in the Appendix A, this filtering operation leads to images characterized by _PSNR_ values closer to those of the images obtained after the first two processing steps of the proposed algorithm, in the conditions under which an improvement of the contours takes place. \begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{2}{c}{**By Adaptive Soft Truncation with**} & \multicolumn{2}{c}{**By Applying the Simplified Algorithm,**} \\  & \multicolumn{2}{c}{**Contextual Modeling (Chang)**} & \multicolumn{2}{c}{**Based on Local Statistics**} \\ \hline
**L** & **PSNR (dB)** & **C (\%)** & **PSNR (dB)** & **C (\%)** \\ \hline
3 & 28.98 & 64.74 & 30.00 & 67.14 \\ \hline
5 & 28.99 & 65.31 & 29.99 & 67.08 \\ \hline
10 & 29.02 & 64.74 & 29.90 & 66.82 \\ \hline
20 & 29.21 & 63.85 & 29.81 & 65.73 \\ \hline
50 & 29.31 & 64.53 & 29.76 & 66.20 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparative results obtained by adaptive soft truncation with contextual modeling and applying the first two steps of our proposed method, in the case of processing only the details sub bands corresponding to the first scale of a wavelet transformation. The side of the analysis window is 2L + 1. Figure 3: Hierarchical correlation maps obtained by the method proposed by [PERSON] and [PERSON] in the case of the House image, \(256\times 256\) pixels. (**a**) Hierarchical correlation map obtained in the case of the original image, not degraded by noise. (**b**) Hierarchical correlation map obtained in the case of the degraded image with Gaussian additive white noise with dispersion \(\sigma\) = 0.05, (PSNR = 26.00 dB). (**c**) Hierarchical correlation map obtained by processing the map from point b with a median-hybrid type filter.