I think they're probably right about the AI-sharpening using specific knowledge about the moon... However, they are wrong about the detail being gone in the gaussian-blurred image.
If they applied a perfect digital gaussian-blur, then that is reversible (except at the edges of the image, which are black in this case anyway). You still lose some detail due to rounding errors, but not nearly as much as you might expect.
A gaussian blur (and several other kinds of blur) are a convolution of the image with a specific blur function. A convolution is equivalent to simply multiplying pointwise the two functions in frequency space. As long as you know the blur function exactly, you can divide the final image by the gaussian function in frequency space and get the original image back (modulo rounding errors).
It is not totally inconceivable that the AI model could have learned to do this deconvolution with the Gaussian blur function, in order to recover more detail from the image.
If they applied a perfect digital gaussian-blur, then that is reversible (except at the edges of the image, which are black in this case anyway). You still lose some detail due to rounding errors, but not nearly as much as you might expect.
A gaussian blur (and several other kinds of blur) are a convolution of the image with a specific blur function. A convolution is equivalent to simply multiplying pointwise the two functions in frequency space. As long as you know the blur function exactly, you can divide the final image by the gaussian function in frequency space and get the original image back (modulo rounding errors).
It is not totally inconceivable that the AI model could have learned to do this deconvolution with the Gaussian blur function, in order to recover more detail from the image.