Holy Mexico, that's some yummy interlacing!
I'm going to do a bit of problem solving here. OK, so initially one would think it would be an easy task... duplicate the gradient in an inverse (or something like that), and apply to video. I realized though, that the gradient filter behaves a little differently than that. For instance, it may darken a pure white area by 25%, but a pure black area won't be darkened at all- it's still recorded as pure black. So herein we have the problem: identifying which areas need to be lightened which amounts. Could be tough.
You probably already knew this... if so, consider this a personal exercise.