Thinking about noise reduction I come up with low pass or band pass filters and using multiple microphones to correlate the signal. However I have no experience, at all.

In the most simple case, simply adding two slightly separated signals should not increase the noise. The problem is, the helicopter sound itself is very noisy, so I'm not sure this would work well. A lot of microphones might be needed, increasing the cost many times.

For low pass filtering, there are mufflers for microphones, did you have those?

Edit: and of course that's not really getting any points in the computer science department.