Well I guess I steered you wrong there--I (for some reason) assumed the typical metal brackets.
If they look like solid ceramic and they're embedded in a tile wall, these could well have been put down with mastic at the same time as the tile. So if you get them out of there, you could have a bit of a chore on your hands regarding the gaping holes. I would probably think twice before doing that.
Now some ceramic brackets are more decorative--and as such ARE connected to metal brackets. I'm beginning to think you don't have these--but you can tell by looking underneath the brackets and seeing if there are formed metal pieces beneath. If it's these, it's easy--as you probably only have to lift them upwards to free them from the brackets.
So, at this point can you tell which it is and get back to us?
-k2 in Colorado