How to remove static, black horizontal lines from footage

I've been combing the internet trying to find a fix for this type of flicker issue, but can only find fixes for rolling, broad bands on footage, but the issue I have is with thin, static dark lines across my footage which I can't find any solution for. See image for example:

Is there any way to fix this without having to create a tonne of masks and lift up the levels of a duplicated clip behind them?? I've tried finding solutions for Premiere Pro and After Effects so any help is much appreciated if there is an effect or method I've not been able to find. 

Thanks in advance!