## 3 Results and Discussion  
In the first stage, experimental determination of the value of the \(k\)-factor was performed. For this purpose, the noisy Shepp-Logan phantom was subjected to wavelet decomposition using a Haar wavelet. A ring artifact reduction process was carried out by changing the value of \(k\) in the range from 5 to 35, and the thresholding level was fixed at \(T=0.4\). Global filtering of the whole sinogram was not performed. The reconstruction result was compared to the reference image using the RMSE and MSE methods. The results of the comparison are presented in the graph in Figure 5. The results presented in the graph show the effect of the \(k\) parameter on the effectiveness of reducing ring artifacts in the Shepp-Logan phantom image. From the graph, it can be seen that the optimal parameter for this phantom is values above 21. A further increase in the value has no effect on reducing the errors between the reference image and the one obtained as a result of processing and reconstruction. After determining the value of the \(k\)-factor, the sensitivity of the presented method of reducing ring artifacts to striations of different intensities was checked. For this purpose, the percentage of introduced noise was increased in the range of 2-20%. Reconstruction was performed and the obtained images were compared to the reference image. Table 2 shows the results of the image comparison for reconstructed images without ring artifact reduction and reconstructed images with artifact reduction. The filtering process used a first-level Haar wavelet, a constant of \(k=21\), a thresholding level of \(T=0.4\) and a span factor of \(N=3\) (Figure 6).The last row of the Table 2 shows the result of comparing the image of the generated phantom and the phantom after reconstruction without introduced artifacts. The analysis of the results presented in the table shows that the reduction in ring artifacts is effective and significantly improves image quality. The results of the MSE method suggest that image noise below 5% as a result of filtering no longer improves image quality. This is due to global filtering, in which, at such a low noise level, the changes resulting from filtering the entire image make more difference than the noise by itself. However, the SSIM and MS-SSIM methods suggest that the filtered image is of similar or even slightly better quality than without filtering at noise levels of 2% AND 5%. With high-intensity stripes, the image has two or even three times the similarity to the reference image.The quantitative results are worse than in the other works cited [2,14], however, it should be noted that in this work the authors use a virtually generated phantom rather than a phantom reconstruction image as a reference image. The filtered back projection (FBP) reconstruction process further introduces some imperfections and simplifications. The work of author [PERSON]. [14] uses reconstruction and iterative filtering which gives much better results. However, it requires many iterations is much time-consuming and has much higher hardware requirements. The method proposed in this work is much easier to implement and has more practical application today. Wavelet decomposition was also performed using wavelet families other than the Haar wavelet. This operation was aimed at checking which of the wavelet families used for decomposition would most precisely identify the vertical stripes and separate them from the non-sine data in the sinogram of the reconstructed object. A phantom with a noise level of 10% was subjected to a series of decompositions. After decomposition, it was subjected to a ring artifact reduction process and compared with the reference image. The results for each phantom are recorded in Table 2 and in the graph (Figure 6).