You should be able to get that out. Try these:
1) I see a very small piece of the stud still protruding above the mount (at about 10 o'clock in your pic). Try using a flat screw driver to push on that in an attempt to get it to unscrew. It's worth a shot.
2) Get a left-hand drill bit about 2/3 to 3/4 the size of the broken off antenna stud. Use a center punch to put a centering hole in that stud. Use the left-hand drill bit to drill a hole at the point you punched. If you're lucky, it will actually unscrew while you are drilling it.
3) If it didn't come out while drilling, us an extractor ("easy-out") of the proper size in the newly drilled hole to unscrew it.