# A New Adaptive Spatial Filtering Method in the Wavelet Domain for Medical Images
## 3 Results and Discussions
The interest in such filters is determined by the fact that much of the existing information in the images is provided by contours, and most of the noise removal methods cause them to fade. Such filters can be designed starting from the finding that near the contours the noise is less noticeable than in the smooth regions, thus being possible to change the filter parameters depending on the level of activity of the processed region. In this case, at the cost of removing a smaller amount of noise in the regions containing contours, they can be better preserved. There is thus a compromise between the amount of noise removed and the quality of preserving the contours in the image. In Table 4, we exemplify the results obtained for the filtration method proposed in two working variants. The first variant proceeds to segment the LL (low level) sub-band of the lowest resolution from a dyadic wavelet decomposition, and depending on the result of the segmentation operation, it chooses a threshold value necessary for the soft truncation of the wavelet coefficients. The method does not require a large computational effort, but the performance obtained by using it is not special. The second method also uses soft truncation of the coefficients, but this time the threshold value is calculated for each coefficient based on local statistics in the wavelet field. On the wavelet coefficients thus obtained, a correction is made according to a contour map determined on the basis of a hierarchical correlation map. Two variants of correction are proposed: a switched correction, in which case either the truncated coefficient is chosen, or the average between the truncated and the unprocessed coefficient, depending on whether or not the respective coefficient belongs to a contour and a continuous correction, in which case a weighted sum of the two wavelet coefficients is performed, the values of the weights being calculated based on the hierarchical correlation coefficient. In the second case, images are obtained with higher PSNR values, especially in conditions of higher noise level, but which have more blurred contours. Figure 4: PSNR and C dependence on the threshold value and noise dispersion (according to data presented in Appendix A). We approached this algorithm in invariant translation form in two ways:  
1. By integrally applying the proposed algorithm in translation invariant form, mediating the results obtained by applying all three processing steps on the cyclic displacements of the input image;
2. By partially applying the proposed algorithm (only steps 1 and 2) in the translation invariant form and performing the correction according to the contour map only on the result thus obtained. It can be observed from the data presented in Table 5, that the invariant approach to translation of the proposed algorithm leads to good results both in terms of PSNR and in terms of contour conservation. Only in one of the cases presented in Table 5 does the initial image have a higher C coefficient than the processed image, otherwise the processed images have a higher C coefficient. This means that with the removal of the noise, an improvement of the contours is obtained.