The one I have isn't identical, but similar. Extremely quiet! Still...... You might try an old trick Yamaha et al used with air cooled 2 stroke engines - bits of rubber to dampen down any ringing between the cylinder fins.
But I think I'd go for a longer hose and putting the compressor outside.
I once solved the problem of a noisy compressor by placing it in another house, and I even got paid for it however, shortly afterwards I did notice an extreme drop in pressure which made my work almost impossible