Subtraction of known background noise
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This would allow voice control for audio players while they are playing. Minor modifications should enable use of hardware equalisers to filter out non-voice frequencies prior to voice recognition.
Finding the right correlation between input and output in amplitude and delay is the mathematical challenge lurking beneath.
Active noise cancellation is quite easy and cheap nowadays. Many headsets (especially bluetooth ones for your phone) already include it. If they work with ALSA, then it will work in simon too.
A software solution would be much harder and in my opinion a bit clumsy in practice. Think about wearing two physical headsets just to capture background noise...