# A New Adaptive Spatial Filtering Method in the Wavelet Domain for Medical Images
## 4 Conclusions  
The interest in wavelet 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 a trade-off between the amount of noise removed and the quality of preserving the contours in the image.  
The article classifies the methods of selective filtering in the wavelet domain according to the statistical modeling of the wavelet coefficients on which these methods are based. Thus, selective filtering methods in the wavelet domain are divided into three groups: methods based on the intra-band dependence of the wavelet coefficients, methods based on the inter-band dependence of the wavelet coefficients and methods based on both the intra-band dependence of the wavelet coefficients and the inter-band one.  
The proposed method uses soft truncation of coefficients, where the threshold value is calculated for each coefficient separately based on local statistics in the wavelet domain. On the wavelet coefficients thus obtained, a correction is made according to a contour map determined on the basis of a hierarchical correlation map.  
The proposed algorithm uses noise dispersion as a parameter, but the switched version needs another parameter, namely the threshold value to obtain the contour map from the hierarchical correlation map.  
Figure 11: Noise reduction from a CT image, using Daubechies scale filter order 4 (db4) [76].  
Figure 10: Noise reduction from a CT image, using Haar wavelet [76].  
Unlike the methods presented in the literature, which in the case of very rich in details images leads to weaker results than soft truncation with optimal threshold values, the proposed method, by soft truncation of wavelet coefficients with threshold value adapted based on local statistics and correction based on the hierarchical correlation map, always leads to better results both in terms of PSNR and in terms of contour conservation.  
Filtration methods mentioned in the literature prove to be very effective in terms of the amount of noise removed from the image, generally leading to high values of PSNR, but this is done at the cost of significant contour degradation. The proposed method leads to close values, although lower in terms of PSNR than other methods, but ensures a much better preservation of contours.  
Conceptualization, M.S.R., C.D. and I.M.; methodology, C.D. and I.M.; software, C.D. and I.M.; validation, M.S.R. and C.F.; formal analysis, C.D.; investigation, I.M. and C.F.; resources, M.S.R.; data curation, M.S.R., C.D., I.M. and C.F.; writing--original draft preparation, C.D.; writing--review and editing, I.M.; visualization, C.D.; supervision, M.S.R. and C.F.; project administration, M.S.R. and C.F. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
This work was supported by a grant from the Romanian Ministry of Research and Innovation, CCCDI-UEFISCDI, project number PN-III-P1-1.2-PCCDI-2017-0776/No. 36 PCCDI/15.03.2018, within PNCDI III.  
The authors declare no conflict of interest.