Bear, I don't know about filtration, but distillation should do it. That'll remove pretty much anything from water, since impurities (i.e., anything but water) can't remain in the water when it changes state from liquid to gas. Of course, if said impurities have a boiling point lower than water, they will boil off first, and depending on your setup you could get them right back in your water anyway. If you could keep the water at 210 F for a while, just in case of anything with a boiling point lower than water, that should do it. I can't think of anything that would be in water that would have a lower boiling point, but it's possible.

Really shouldn't be that hard to make a still for this kind of thing, either. A tea kettle or pressure cooker, some copper tubing, and whatever you want the water to go into for storage.

I might have to try this sometime.