Why not using 3 mikes?

Install 3 mikes side by side in a triangular assembly, all of them
pointing to your mouth. Noise sources are not directly in front of the
mikes, so they will arrive at different times (phases) between those
mikes. So, the trick is just subtract signals one mike to another, in 3
different subtraction circuits, the resultant is exactly the noise
sensed between each two mikes, invert this signal and subtract each
result from the original signal from the two correspondent mikes and
voil‡, you have your pure voice over "some" flat noise base level,
remove the "almost" dc constant, you have your voice.

Another suggestion is to install one mike as your mouth piece, other two
a little apart, those two will identify the noise signal and remove it
from the mouth piece signal.  Of course there is a phase shift problem
in this solution, but even so noise would be reduced.

No time to develop a math solution to exercise the above examples,
perhaps someone else?

Wagner.