## 4 Conclusions  
The results presented in this paper show a method of reducing ring artifacts that effectively improves the image in which ring artifacts of different intensities occur. De  
Figure 7: Graph showing results of comparative analysis of images after reconstruction using wavelets of different families and reference image using RMSE, SSIM and MS-SSIM methods. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Wavelets Type** & **PSNR (dB)** & **RMSE** & **SSIM** & **MS-SSIM** \\ \hline Biorthogonal 5.5 & 29.0492 & 0.1476 & 0.6543 & 0.7451 \\ Biorthogonal 6.8 & 29.0364 & 0.1481 & 0.6295 & 0.7083 \\ Daubechies 2 & 29.0415 & **0.1479** & **0.7700** & **0.8080** \\ Daubechies 10 & 29.0353 & 0.1481 & 0.6633 & 0.7551 \\ Daubechies 20 & 29.0182 & 0.1487 & 0.6293 & 0.7366 \\ Daubechies 30 & 28.9943 & 0.1495 & 0.6604 & 0.7428 \\ Symlets 4 & 29.0808 & 0.1465 & 0.7276 & 0.7685 \\ Symlets 8 & 29.0652 & 0.1471 & 0.6702 & 0.7565 \\ Symlets 12 & 29.0140 & 0.1488 & 0.6183 & 0.7119 \\ Symlets 16 & 29.0317 & 0.1482 & 0.6243 & 0.7255 \\ Symlets 20 & 29.0633 & 0.1471 & 0.6309 & 0.7397 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._pending on the intensity of the ring artifacts, the results obtained were up to 50% better than the image not subjected to any filtering. The comparison uses a computer-generated cross-sectional image as a reference, rather than a noise-free reconstructed phantom image. This causes the comparison results to be lower, due to the fact that the reconstruction itself introduces other errors and imperfections in the image, not only ring artifacts. The FBP method is not perfect and introduces some approximations to the calculation. The authors made a comparison between the phantom and various reconstruction methods in their earlier paper [21]. The authors intend in this way to show the level of imperfection of the image relative to the real object. An important aspect to pay attention to when performing reduction is the selection of the k parameter. Its imprecise selection can significantly reduce the effectiveness of the method. The need for experimental selection of the parameter k is a drawback of the model; therefore, further research based on varied real data should parametrize this parameter for different materials. A second filtering step based on EMD introduces changes to all pixels in the image, as shown by the comparative results for very slight artifacts (less than 5%). The authors want to conduct further research to develop this method to provide it with more selective performance. Performing a test of different wavelet families in wavelet decomposition showed that the complexity of the wavelet has a negative effect on the effectiveness of artifact reduction. The best results were obtained using the following wavelets: Haar, Coiflet 1, Biorthogonal 2.2 and 3.1 and Daubechies 2. The lowest efficiency was obtained by performing artifact reduction with the \"Discrete\" Meyers wavelet. Greater variation in the results for individual wavelets is expected when reducing ring artifacts in real images due to the greater complexity of such images. This type of work is planned in further work on artifact reduction in tomographic images. The authors are in the process of testing the method on real data obtained from the micro-CT Skyscan 1172, and the results of this work will be presented in the authors' next article. Conceptualization, P.L., M.B. and A.D.-G.; methodology, P.L. and M.B. ; software, P.L. ; validation, P.L. and M.B. ; formal analysis, M.B. and A.D.-G.; investigation, P.L. ; resources, P.L. ; data curation, P.L. ; writing--original draft preparation, P.L. ; writing--review and editing, M.B. and A.D.-G.; visualization, P.L. ; supervision, M.B. ; project administration, P.L. ; funding acquisition, P.L. All authors have read and agreed to the published version of the manuscript. This work was supported by the Ministry of Science and Higher Education of Poland under research project No. WI/WM-IIB/8/2023. Not applicable.