## 3 Results  
Figure 5 reports the validation and training losses for the three Unets and the two acquisition scenarios, illustrating that, in all six cases, these networks exhibit rather quick convergence. The training losses for all cases converge in the first couple of epochs (Figure 5a,b); however, a gradual reduction in loss can be seen for all three networks throughout the training, while the validation losses converge by the 20 th epoch (Figure 5c,d), i.e., a plateau is reached and then the loss fluctuates, which is the desired observation. Specifically, the validation losses for the AUNet and RUNet converge by the 15 th epoch for the With-Prior scenario and by the 20 th epoch for the WithOut-Prior scenario. Notably, the DUNet validation loss converges within the first four epochs; this may be related to the use of dense convolutional layers that can carry the outputs of one convolutional layer to all the future layers allowing the network to learn more complex representations of the images [33, 52]. Tables 1-3 review the results from all studies corresponding to upscaling LQ-to-HQ images that were downsampled to 1/8, 1/4, and 1/2 of the complete matrix, respectively. Each table reports the results for the two scanning scenarios, and for 100 and 1000 epochs of training for each scenario. The first general observation is that, for the same scanning scenario and the same downsampled matrix, as observed by the values of the descriptive statistics, the three UNets exhibit somewhat similar performances, as reflected by the mean MSE, MIE, SSI, and PSNR values. This is an intriguing observation, indicating that all three choices of UNet perform similarly when sufficient training is performed. Figure 6 also shows that, for the same scanning scenarios, and the same downsampled image, there is virtually no difference between training for 100 or 1000 epochs. Figure 5: Representative results from the training sessions depicting the training (**a,b**) and the validation (**c,d**) losses (as log mean squared error versus epochs) for the two acquisition scenarios: With-Prior (**a,c**) and the WithOut-Prior (**b,d**) information. These examples correspond to the worst-case scenario of upscaling 1/8 downsampled synLQ images toward the corresponding 176 \(\times\) 208 synHQ. The networks were trained for 100 and 1000 epochs; the first 100 epochs are presented here. Substantial differences in performance of the UNets, however, are observed when comparing the two acquisition scenarios, as can be clearly seen in Tables 1-3, and in Figure 6. As compared to the cases of With-Prior, upscaling of downsampled LQ images with the WithOut-Prior scenario exhibit lower SSIM, higher MSE, higher MIE, and lower PSNR, i.e., the performance of the UNet WithOut-Prior is worse than that of With-Prior. In the With-Prior cases, the physically collected (and augmented) augmMRI provide additional anatomical and morphological data about the same structures in the object, resulting in upscaling being closer to the ground truth synHQ (i.e., complete matrix with reduced noise), as also reported in [21]. The LQ images at the WithOut-Prior scenario can also be upscaled to a different degree, depending on the size of the synLQ. Indeed, when the cases of WithOut-Prior are considered (the graphs in the two leftmost columns), the UNets upscale 1/8 downsampled images with lower accuracy. This result reflects the fact that at  
Figure 6: Performance of the three UNet architectures (RUNet in red, DUNet in black, and AUNet in Green) for the two With- and WithOut-Prior acquisition scenarios after training for 100 and 1000 epochs. (**a**) Mean Structural Similarity Index, (**b**) Mean Squared Error, (**c**) Mean Intensity Error, and (**d**) Peak Signal-to-Noise Ratio of reconHQ vs. synHQ, for different sizes of input synLQ images. The measures are reported as average (standard deviation) for N = 540 test images corresponding to 84 subjects. lower resolution (larger voxel size) finer structural details may be lost.