NoiseTorch is another recent discovery that can help you remove background noise in real-time while recording with a microphone on Linux.
Much like Cadmus which we covered recently and were very impressed with, it makes use of the Real-time Noise Suppression Plugin for PulseAudio based on Xiph's RNNoise (a noise suppression library based on a recurrent neural network).
The application gives you pretty much a one-click solution, as it sets it all up for you and then you can just select NoiseTorch as the microphone source and away you go. Just like we did with Cadmus in the above link, here's a test of its ability to cut out some harsh noise.
While it seems Cadmus does a slightly better job at reducing background noise while chatting, overall it still pretty much does the job you need it to. Unlike the test, you're not usually going to have someone taking a hammer to the desk the microphone is attached to but it's interesting to see how these tools do in extremes. It should nicely get rid of all that crisp eating, furious typing and vaping noises for you.
Do you want to try it out yourself? You can find NoiseTorch on GitHub.