Interesting. I would like to see that done. I don’t think it would be as trivial as simply reverse engineering a gaussian blur and doing the obverse of the setting to put it back.
Once the data is destroyed (as it would be in a jpg once you apply the blur and save the image) the data is gone.
The analogy would be a picture that was not exposed correctly. There is a limit to the amount of manipulation that can be done on an image if the data simply isn’t there. If someone is wearing a black shirt and the basic image doesn’t have enough shades of gray to distinguish detail, then you will never get the detail out because it isn’t there to begin with.