You can use filters, probably low-pass filters or band-stop filters, as a fair bit of gradient noise tends to be above the key frequency ranges used by humans. You might need to get a bit creative as the slice repositioning noises are low enough frequency for there to be meaningful overlap. The "clunk" from the coil relaxation is, if I recall, within normal human speech range, but relatively distinctive.
One problem is that a portion of fmri scanner noise tends towards white noise, crossing the key human frequencies. You might be able to use techniques such as median filtering to reduce the white-ish noise.
Darn, it's too late at night for me to remember what causes the white-ish noise. It has been years since I last went in while the scanner was operating, and I could be mis-remembering. On the other hand, the movement of the coils in a device like that is going to generate some turbulent air flow that should come out as white-ish noise, I think.
Note: I was around research mri scanners. No pretty cover, and acoustic noise baffling was not the first priority.
