Hmmm>>>I recently began experiencing a vibration just as you describe, though I wouldn't call the noise "loud" but it is annoying. So far, all I know is that any of the following temporarily ceases the vibration for several seconds:

1) turn the wheel slightly
2) let off and reapply the brakes

I can't figure out the cause either, but I'm working on it...As of now, I suspect a brake caliper/pad problem, sway bar bushing, power steering pump pulsing, tierod end problem, something loose in the dash.

Good luck! Post if you solve this one...