Even if you do not know the minimum and maximum you can try common normalizations like subtracting the mean and dividing by the standard deviation. I’m not sure if the particular type of normalization is important, but you must match the normalization between the training and test set. That means using the mean and variance computed on the training set even if it is not exactly the mean and standard deviation of the test set.


This seems like a tricky problem overall but you might consider adding more data augmentations or noise to your simulated dataset to make your model more robust. Are your simulated images LR simply degraded HR images? You might consider some more sophisticated augmentations from libraries such as albumentations.


If your current amount of real data is small, then data augmentations should help a bit. However, a sanity check you can do at this stage is see if your model can overfit your training data and perfectly reconstruct a small training set.