This would be a useful function to have for live performances. I have two ideas off the top of my head, but am not too optimistic about them:

1. subtract a loop of the 'quiet' room from the live input. This is simple but probably wouldn't work too well because, if there is any irregularity at all in the recording, this will create an audible pattern.

2. take the 'quiet' room recording and put it into a [sigmund~]. Keep the highest amplitude value in the loop for each frequency band and use this to set the strength of a notch filter for the respective band. I've got a bad feeling about this idea- like it'd work well with clear, isolated pitches, but probably not with noise (which is going to be the main thing you want to filter!)

@s.elliot.perez This was an attempt from a few years ago....... not mine..... background noise filter.zip
It might have some useful pointers.
1 will not work.
2 will work, especially if the room has frequencies that resonate, but will not filter all noise, which changes all the time. It will be an automatic equaliser in effect.
The patches posted above take that idea, and elaborate.
Sabine "feedback killers" also used automatic notch filters.

You could try cancellation by phase inversion, bypassed as a threshold is met so as to pass "non background" noise, but it will be no more effective than a noise gate.... and will introduce nasty artefacts.

Noise cancelling headphones work by phase inversion, but the program material is known and so can bypass the function. With live microphones that is not an option.
David.

@JosephEoff @svanya take the multiband filter approach: https://forum.pdpatchrepo.info/topic/10268/what-s-your-favorite-noisegate/6

@s-elliot-perez If you haven't already, you might want to check out I04.noisegate in Pd's documentation, which is an FFT-based approach to what you're looking for. It does produce artifacts if you push it too far, but I don't think any real-world noise filter can be perfect unless you live in a universe of only sin waves~~~~~

Also a +1 for @lacuna's suggestion, I tried out that multiband filter to prevent feedback when using an open mic. It's computationally expensive, but it works nicely.