I think this is a very common problem, but I cannot find a suitable solution for me. As you all know, WP supports a dark and a light theme. The user can change the theme and the
Detect the theme (Supporting dark and light themes gives the best solution for this, I think), and then set the image accordingly. If you do this a lot, a custom control where you can supply two image sources and the correct one gets used would be easy enough to create.
Edit: Here's another good article on this topic. New Screen Resolutions