## 5 Discussion  
As shown in Table 2, the proposed G-SSIM method with node grouping depths of 1 and 2 demonstrates the most effective error reduction, i.e., the smallest number of LQ images assigned better scores than the HQ images. However, increasing the G-SSIM node grouping depth to 3 significantly increased errors, as depicted in Figure 9a. Figure 11: Comparison of the GQA scores for the Low-Quality (LQ) and High-Quality (HQ) reconstructions of the considered phantoms. Figure 10: Sample phantoms (**a**) and their High-Quality (**b**) and Low-Quality (**c**) reconstructions. While the average execution time for the G-SSIM methods was relatively high across all the evaluated variants, Figure 9a clearly shows a substantial increase in execution time when the node grouping depth was increased to 3. Figure 9b illustrates a correlation between deeper node grouping and increased errors for the Group PSNR method. This effect might be due to deeper node groups encompassing more nodes, potentially complicating the the similarity assessment. Interestingly, the classic PSNR method outperformed its grouped variant regarding error reduction. For depths 1 and 2, the classic PSNR was the second-most-effective choice after the group SSIM methods. Regarding average execution time, the PSNR method was the fastest among the examined GQA methods (see Table 2). Despite variations in average execution time observed across different depths of node grouping in Figure 9b, the group PSNR variant maintained a relatively low average execution time overall. The Histogram Comparison method consistently encountered significant benchmarking errors. Increasing histogram precision directly correlated with increased error occurrences (see Table 2). While the average execution time remained relatively low across all the tested variants, the method's overall performance was notably sub-par. When the selected phantom examples are considered, the PSNR family methods and Histogram Comparisons with precisions of 0.01 and 0.001 assigned higher similarity values to the LQ results, while the G-SSIM family methods and Histogram Comparison with a precision of 0.1 assigned higher similarity values to the HQ results (see Figure 10). As seen in Figure 10, for the two-balls, the rod, and the side-ball phantoms, a visual assessment makes it challenging to definitively determine which reconstruction was closer to the phantom. Consequently, the interpretation of the similarity results is also ambiguous. While the HQ and LQ similarities were close for the two-balls phantom, the HQ slightly exceeded the LQ for most GQA methods, except for the Histogram Comparisons at 0.01 and 0.001 precision. This likely stemmed from the faint connection between the balls in the scan images, absent in the phantom. The Low-Quality image exhibits a more pronounced unwanted connection. The visual similarity aligns with the previous phantom observations. This is to be expected, as both phantoms consisted of ball shapes. For the H phantom, the scan images are noticeably distorted compared to the phantom. The H shape is deformed in both scan images, and the Low-Quality image lacks red spots. Conversely, the High-Quality image has red areas resembling the H's vertical rods. The scan images for the H phantom are less similar to the phantom than those of the ball phantoms. However, there is a greater similarity between the High-Quality and Low-Quality images. The numerical results generally align with the visual observations, except for the Histogram Comparisons at 0.01 and 0.001 precision. The HQ results are significantly higher than the LQ results. For the rod phantom, while the scan images differ, it is challenging to determine which is closer to the phantom. The rod shape is well preserved in both, but the red spots are distributed differently. The High-Quality image has a denser red center, while the Low-Quality image has red spots that are more evenly spread. The GQA method results for the different quality scan images vary.