## 3 Results
Such finer structures; however, may be recoverable by the UNet in With-Prior scenario in the case that they are preserved in the augmMRI image. The performance of the UNets may also be appreciated in Figures 7 and 8, which show the reconHQ images together with pixel-by-pixel differences with respect to the ground truth (i.e., \(|\) reconHQ--synHQ\(|\)) for the three networks at different synLQ sizes and two scanning scenarios. It can be observed that lesion reconstruction is better in the With-Prior compared to WithOut-Prior acquisition scenario for the 1/8 downsampled synLQ. Figure 7: Representative example of reconstructed images and errors versus ground truth with the three UNets trained for 100 epochs with the With-Prior acquisition scenario (i.e., including the augmMRI) to upscale (**a**) 1/8 downsampled (22 \(\times\) 26) and (**b**) 1/4 downsampled (44 \(\times\) 52) and (**c**) 1/2 downsampled (88 \(\times\) 104) synLQ. The Error intensity in this figure is five times the original intensity. Table 4 shows the results for the F-ratio obtained for fixed effects in the MEM. The F-ratio corresponds to the F-test performed in the mixed-effect model that was fitted each time. For more information one can refer to [43]. In the freeware R, which was used to fit the models, F-test values can be derived using the anova(.) option for a fitted model lmer(.) from the library lme4. We test the significance of type of UNet, matrix size and the interaction of the type of UNet and the matrix size. We provide the F-ratios for each of the terms that were used in each mixed effect model. The observed F-ratios are very large, and as a result, all of their respective \(p\)-values were well below 0.01 (the level of  
Figure 8: Representative example of reconstructed images and errors versus ground truth with the three UNets trained for 100 epochs with the WithOut-Prior acquisition scenario (i.e., not including the augmMRI) to upscale (**a**) 1/8 downsampled (22 \(\times\) 26) and (**b**) 1/4 downsampled (44 \(\times\) 52) and (**c**) 1/2 downsampled (88 \(\times\) 104) synLQ. The error intensity in this figure is three times the original intensity. significance alpha), which means that the type of UNet, the input matrix size, and their interaction are all highly statistically significant factors. Therefore, we only present F-ratios and not the \(p\)-values in the table, as the latter in all cases would have been identical, i.e., << 0.01. The actual interaction plot between the fixed variables can be observed in Figure 9 for With-Prior and WithOut-Prior acquisition scenario, indicating the relative performance for every response metric for all possible combination of the two factors that we examine in our mixed effect model. Inspection of WithOut-Prior data sets that resulted in reconstructions that exhibited lower scores (SSIM less than 83% for 1/8 matrix and less than 91% for 1/4 matrix) pointed to the anticipated effect of lesion size and contrast relative to the neighboring tissue, representative examples of which are shown in Figure 10. Figure 10 shows a case where the lesion is rather large (greater than 8 pixels in a single dimension) and the intensity of the lesion is significantly higher than neighboring pixel values (greater than 100 on a 0-255 scale). Figure 10 corresponds to cases that the lesion (i) is not observed in the upscaled images (reconHQ) that were reconstructed from the 1/8 downsampled synLQ images for the WithOut-Prior acquisition scenario, and (ii) is observable (arrow) in the