Yes, my point is that it depends a lot on the specific blurring. If you just average a square neighborhood of 4 pixels around the center, and add no noise, it is very likely that you can "enhance" the resolution back to almost the original image. Yet, if the blur kernel is much larger (say, a gaussian of width 40 pixels), and you add some noise after te blur, it is very likely that you have completely destroyed the information.