Unless you’re using floating point numbers and have padded the image to infinity, it’s literally untrue that applying a Gaussian kernel doesn’t throw away at least some (if not a lot of) information. I think what you intended to say is the blur doesn’t remove “all” the information. Not to mention he downsized the image (likely using bilinear not even bicubic ) further throwing out a ton of information. Not to mention he then showed the image on a display and took a photo from across the room. For all practical purposes the technically incorrect pedantic statement does not apply even if you correct it.

Looking at the images, it will be fantastical if not a violation of information theory if the phone didn’t use prior information about how the moon looks to create the photo.

Source: spent way more months than I would have preferred calculating CRLB values on Gaussian blurred point source images.