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I just upgraded Topaz Photo AI to version 3 and decided to explore it.
As a Photoshop plug-in it has de-noise and sharpen features as well as face recognition w/ detail enhancement AI. As a stand-alone it can also act like Gigapixel.
I haven't used it on extremely poor quality images yet but it works extremely well on this good quality shot. Stand-alone Photo AI was used to enhance & up-scale this image to 16,000 px x 10.600 px (168 MP).
This is a ludicrously tight crop of my granddaughter on her way to her senior prom. You can see a tiny superimposed representation of the full frame in the upper left corner.
The defects are there but considering the 2x enlargement viewed at 100%, and taken with a hand-held zoom lens, this is more than sufficient for most purposes.

Truth in advertising: I slightly smoothed out the micro skin creases just under her left eye. Sometimes 'truth' can be too much.
Under this level of scrutiny, I find it interesting just how shallow DOF at f5.6 can be given the distance-to-subject. The bridge of the nose has not been smoothed out