I have the same problem with a different DAW Cubase SX and I too have the Line 6 UX2. The weird thing is it only happens on certain songs and if I move them to a different location on my hard drive the noise sometimes goes away!

Maybe the suggestions on the Line 6 forum may help you HERE

I tried the suggestions but nothing seemed to work altho the noise occurs less these days.

If you get successful please post what you did as I will also.
Frustrating init!!

Alyn