## 3 Results and Discussion
Figure 5: A graph showing the result of comparing images of the reference Shepp–Logan phantom and the reconstructed noisy and filtered image of the Shepp–Logan phantom using the RMSE (red line) and MSE (black line) methods for changing parameter k.  
When analyzing the results, it should be noted that with the RMSE method, the similarity coefficient tends to 0, so the lower the value, the more similar the obtained image is to the reference image. In the case of the SSIM and MS-SSIM methods, the values tend to 1, that is, the closer the value is to one, the greater the similarity of the images. In the results shown in the Table 3 and Figure 7, you can see four wavelets that obtained significantly higher results than the others: Haar, Coiflet 1, Biorthogonal 2.2 and 3.1 and Daubechies 2. The values of the coefficients are included in Table 3, and the four mentioned wavelets are in bold. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **PSNR (dB)** & **MSE** & **SSIM** & **MS-SSIM** \\ \hline No Filtration 20\% noise & 21.99288 & 0.07074 & 0.37611 & 0.60218 \\ Filtered 20\% noise & 27.09104 & 0.02187 & 0.80090 & 0.82214 \\ No Filtration 10\% noise & 27.08707 & 0.02189 & 0.47612 & 0.76688 \\ Filtered 10\% noise & 29.35344 & 0.01299 & 0.80226 & 0.82219 \\ No Filtration 5\% noise & 34.59004 & 0.00389 & 0.61120 & 0.80143 \\ Filtered 5\% noise & 27.08509 & 0.02190 & 0.80265 & 0.82261 \\ No Filtration 2\% noise & 37.74795 & 0.00188 & 0.79428 & 0.88367 \\ Filtered 2\% noise & 27.09303 & 0.02186 & 0.80534 & 0.82340 \\ Noise-free reconstruction & 38.61433 & 0.00154 & 0.92164 & 0.98685 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of calculated similarity coefficients of the post-filtered and noisy unfiltered images of the Sheep-Logan phantom to the reference image. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Wavelets Type** & **PSNR (dB)** & **RMSE** & **SSIM** & **MS-SSIM** \\ \hline Haar & 29.0471 & **0.1477** & **0.8031** & **0.8231** \\ “Discrete” Meyer & 28.9729 & 0.1502 & 0.6140 & 0.7211 \\ Coiflets 1 & 29.0710 & **0.1469** & **0.7898** & **0.8155** \\ Coiflets 5 & 29.0279 & 0.1483 & 0.6337 & 0.7244 \\ Coiflets 10 & 29.,0420 & 0.1479 & 0.6533 & 0.7484 \\ Coiflets 15 & 29.0320 & 0.1482 & 0.6434 & 0.7320 \\ Biorthogonal 1.5 & 29.0743 & 0.1468 & 0.6708 & 0.7485 \\ Biorthogonal 2.2 & 29.0660 & **0.1470** & **0.7631** & **0.8052** \\ Biorthogonal 2.8 & 29.0713 & 0.1469 & 0.6531 & 0.7320 \\ Biorthogonal 3.1 & 29.0513 & **0.1475** & **0.7833** & **0.8125** \\ Biorthogonal 3.9 & 29.0886 & 0.1463 & 0.6601 & 0.7470 \\ Biorthogonal 4.4 & 29.1073 & 0.1457 & 0.7111 & 0.7823 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Table showing results of comparative analysis of reconstructed images using wavelets of different families and reference image using RMSE, SSIM and MS-SSIM methods. The results with the highest similarity values to the reference image are shown in bold. Figure 6: Images showing Shepp–Logan phantom reconstructions (**a**) without ring artifact reduction (stripe level 10%) and (**b**) after performing ring artifact reduction with constant k = 21, thresholding level T = 0.4, and span factor N = 3. It can be noted that the more complex the wavelet, the lower the similarity to the reference image obtained. The lowest efficiency was obtained by performing artifact reduction with the \"Discrete\" Meyers wavelet. The use of global filtering of the entire image may also have affected the values obtained. A slight reduction in the value of all pixels relative to the reference image is visible in the results as a lower similarity even though the morphometric information of the image was not lost.