## 3 Results
### Impact of Compression Artifacts Removal on Nuclei Segmentation  
The main purpose of removing compression artifacts from HE-stained images is to improve the performance of further analysis, e.g., segmentation of cell nuclei. We tested the performance of the nuclei segmentation using Hover-Net and STARDIST models after the application of the four best artifact removal methods. Two datasets were used in this analysis: Kumar and CPM-17. We calculated the difference between the performance scores obtained for each image processed without removing compression artifacts (marked as no correction) and images after removal. Table 3 and box plots in Figures 6 and 7, contain the outcomes of selected segmentation measures for both nuclei segmentation methods. We conducted a Wilcoxon test to determine if the results were statistically significant. The p-values for each measure are shown in the Table 4. The developed methods improved the results, particularly considering the \(PQ\) measure. Figure 8 presents the example segmented images for both datasets with Hover-Net models. Figure 5: Results of the best methods for Set5, Set14, Kodak24, LIVE1 and BSDS500 datasets. Images present: original image, compressed image \(QF=30\), EPIIC, EPIIC Sobel, FBCNN, image after Gaussian smoothing, guided filtering. As can be seen for some nuclei, the EPIIC and EPIIC Sobel methods allowed more precise nuclei detection. It can also be seen that some instances that were not detected by the no-correction Hover-Net model were detected after artifacts removal. In addition, note the results of image segmentation after removing compression artifacts with the Guided filter. For the first of the presented image fragments from the CPM-17 set, a sizable section between the nuclei with irregular outlines was marked as the nucleus area. Such a phenomenon can be a significant obstacle in using this algorithm to remove compression artifacts. Moreover, the median differences of \(DICE\), \(AJI\), and \(PQ\) for this method do not indicate such significant differences in segmentation results. The FBCNN network allowed for enhanced image quality, but for most images, it caused the degradation of the segmentation performance for both tested segmentation models. The developed edge-preserving algorithms also achieved slightly better results than the Gaussian filter with the same parameters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** &
\begin{tabular}{c} **Segmentation** \\ **Method** \\ \end{tabular} & **Method** & \(DICE\) & \(AJI\) & \(PQ\) \\ \hline \multirow{4}{*}{**CPM-17**} & **Hover-Net** & **EPIIC** & \(2.052\times 10^{-1}\) & \(5.037\times 10^{-1}\) & \(2.270\times 10^{-1}\) \\  & **EPIIC Sobel** & \(1.391\times 10^{-1}\) & \(8.888\times 10^{-2}\) & \(6.440\times 10^{-2}\) \\ \cline{2-6}  & **STARDIST** & **EPIIC** & \(1.024\times 10^{-1}\) & \(4.540\times 10^{-2}\) & \(1.500\times 10^{-3}\) \\  & **EPIIC Sobel** & \(9.840\times 10^{-2}\) & \(4.700\times 10^{-3}\) & \(8.19\times 10^{-5}\) \\ \hline \multirow{4}{*}{**Kumar**} & **Hover-Net** & **EPIIC** & \(1.206\times 10^{-1}\) & \(3.349\times 10^{-1}\) & \(4.300\times 10^{-3}\) \\  & **EPIIC Sobel** & \(4.039\times 10^{-1}\) & \(7.292\times 10^{-1}\) & \(5.020\times 10^{-2}\) \\ \cline{2-6}  & **STARDIST** & **EPIIC** & \(3.910\times 10^{-1}\) & \(3.910\times 10^{-1}\) & \(7.609\times 10^{-1}\) \\ \cline{2-6}  & **EPIIC Sobel** & \(2.958\times 10^{-1}\) & \(8.552\times 10^{-1}\) & \(3.575\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The table presents the \(p\)-values of the Wilcoxon test.