## 4 Discussion  
The ability of UNets to create an image-to-image translation makes them a suitable neural network model for improving low quality MR images post acquisition. As demonstrated herein and in prior works [21; 22; 23; 24; 25; 26; 27], UNets can be designed and then trained to seek features between pairs of LQ and HQ MRI of the same exact view of the same object; the trained UNet can then be used to upscale a new LQ to its (unknown) HQ image. This performance may relate to the endogenous capability of UNet architectures to identify anatomical and/or morphological features [21; 22; 23; 24; 25; 26; 27; 28; 33; 34; 35], which are the basis for accurately describing a pixel-by-pixel transformation between the downsampled noisy LQ image and the complete matrix HQ one. Moreover, in this work, since the UNets were trained with noiseless ground truths, i.e., the synthesized synHQ images, the reconstructed upscaled images were noiseless. This denoising action is a direct highlight of the fact that the features and quality of the reconstructed images depends on the corresponding features and quality of ground truths. The tested UNets indicated several common characteristics. First, all three UNets exhibited similar performance manifested by summary statistics when trained and tested for the same data sets, for the same downsampled original images (the synLQ images) and the same acquisition scenario. This was a rather unexpected outcome; it suggests that the UNet architecture might be a robust backbone for revealing structural image features, irrespective of the variations in the architecture of the individual networks. Another observation is that all three UNets converged within the 25 th epoch (Figure 5). This is also evident from Tables 1-3, which report performance of the three UNets after 100 and 1000 epochs: there is no significant improvement in any of the four evaluation metrics. For example, the training losses at 100 and 1000 epochs differ by 0.0002/1.0, while the validation losses are less than 0.0001/1.0. The primary difference between them was that DUNet training and validation losses indicated convergence within the first couple of epochs. The origin of this rather rapid convergence was not identified. The outcomes of these studies further emphasize that the effectiveness of upscaling with the studied UNets depends on the actual image acquisition parameters, such as: (i) the matrix size of the downsampled image; (ii) the structure(s) of interest, including their size relative to the spatial resolution of the downsampled image, and their contrast relative to the surrounding matter; and (iii) whether a complementary image was available (or in an actual study, was acquired and included in the network training). As reflected in Tables 1-3, the synLQ matrix size affected upscaling and, as expected, the worst performance corresponded to upscaling the 1/8 downsampled images. Based on the structural similarity indexes, UNet-upscaled 1/2, and 1/4 downsampled images exhibited up to 95% \(\pm\) 0.50% and 93.24% \(\pm\) 0.73% similarity, respectively, with respect to the ground truth in the worst-case scenario of WithOut-Prior. In contrast, the 1/8 downsampled images, when upscaled with the WithOut-Prior acquisition scenario, had a similarity of 84% \(\pm\) 1.5% to the ground truth. Notably, when complementary priors were used, the UNet upscaled 1/8 downsampled had a 97% \(\pm\) 0.40% similarity to the ground truth. While the reported metrics offer a useful quantitative performance of the upscaling, as statistical entities calculated over the entire image, these metrics do not provide information about the success of upscaling details of structures. Indeed, inspecting data sets with low similarity indices, it became apparent that the UNets were not accurately reproducing the margins of lesions or edges of white and gray matter (Figure 8a-c).