Let's say I a perform convolution of an image with a Gaussian kernel of some size.
Is it possible to produce the exact same result from a downscaled version of the image? If so, what's its minimal size?
I'm not looking for an exact answer, some directions where I should start looking are enough. (I have some basic DSP and image processing knowledge but not much beyond that.)
Edit: A closely related question is - does Gaussian blur lose information, i.e. is it impossible to reconstruct the original from the blurred image?