Solving CPU noise from USB audio interface?

I've got a fairly cheap interface (PreSonus AudioBox USB), and whenever I try to record something, the signal comes with a lot of horrendous CPU noise (like a high pitched whine/chatter).

Would a better interface solve this problem? I've got my whole audio setup plugged into one power strip (nothing fancy) so it doesn't seem like a grounding issue (although I was getting the noise through my monitors until I cut the grounding pin off the power cables for the speakers, so I'm not sure). I've also seen it mentioned that running the USB out from the interface into a powered USB hub could help.

Any ideas?