> What you are left with is the edges (high frequency)
So you subtract a slightly phase shifted high frequency signal, you're left with a high frequency signal that may be amplified at the edges depending on your phase shift. Nothing surprising here?
The question is can you create a high frequency residual by subtracting a lowpass filtered (gaussian blur?) image? I don't think so. You're just left with whatever high frequencies you had but you aren't creating any new ones.