(These are my humbly presented thoughts, I am certainly no expert) The crux of any method of differentiating the user's signal from background noise, I imagine

(These are my humbly presented thoughts, I am certainly no expert) The crux of any method of differentiating the user's signal from background noise, I imagine, would look to leverage data that has a higher signal-to-noise ratio than the naive microphone recording of the environment. At a high level this is how I would expect we humans do this. We have some sort of sensory data from us feeling the vibrations of our voice, and use this to "factor out" our own voice from what our ears perceive. In terms of how this might work to factor background noise out of a microphone recording, if we had some kind of hardware (phone, smartwatch, keyboard) that is able to sense the vibrations of the user's voice (via phone in the pocket, watch on the wrist, keyboard that you're resting your palms on as you type), we might be able to use some signal processing algorithms with that signal and the environmental noise to factor out the user's voice. (One might ask "well why not just use the signal from the hardware then?". In terms of quality, I'm not sure if it would be enough---intuitively, I'm guessing it might sound muffled if you played back the recordings of your voice as picked up by your palms resting on a keyboard. But, it might be good enough data that we can use some signal processing algorithm to tune our noisey, but high-quality, data for the user's voice.)