Backyard Aquaponics
A place to discuss aquaponics

Yup, still one of the best purifying techniques for water - Distillation.

theoretically, you could evaporate the water to the point where the salt concentration is so high that it precipitates out and crystalises on the bottom. Then if you decant the water, rehydrate it with the distillate, you'll be minus the salt but still have a relatively high content of nutes and other things. Maybe.
But either way this is too labour intensive to be useful

Slightly OT, but would setting up a still on a normal sea water aquarium purify the water enough to remove all ammonia etc and keep the fish alive?
It would also serve to heat the water (maybe too much)

This might do away with a biofilter and then also the problems with excess nitrogen?

again I am not talking AP here. Anyway just a random thought that came to me.