It has been proven that guns don't kill people, mentally ill people with guns kill people. Since keeping the mentally ill from procuring firearms should be a top priority in this country, I think both sides can get behind a bill requiring all gun owners, current or prospective, to undergo psychiatric testing as a prerequisite to owning firearms.
This would be a one time exam for each individual, after which he would be free to purchase weapons and keep his current collection. Obviously, if a current gun owner fails the exam he would be expected to give up his weapons. If he refuses to do so, a humane solution might be to put him on a national "Armed and Disturbed" watch list.
It's the only way to be sure, and if and if you're not crazy, obviously you have nothing to worry about, right?