It occurs to me that one could use similar sub-pixel techniques used by ClearType to improve the resolution of graphics as well as text. One way to do this would be to downsample an image using a kernel with different horizontal phases for red, green and blue. However, this wouldn't take into account the fact that when making one pixel red, you need to make a nearby one cyan to avoid annoying fringes. With text, the geometry can be controlled so that the widths of horizontal spans are always a multiple of 3 subpixels, but if you're starting with a bitmap you can't really adjust the geometry. Perhaps it wouldn't matter in practice: the same effect happens with NTSC television signals - if you get a black and white pattern with horizontal frequency components in the chroma band you'll get colour fringes for exactly the same reason, but you usually don't notice it because for most images it evens out on average.
I'll have to do some experiments and see what happens.