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No, your brain can not do this in the same way...

The ability to extract a signal below ambient noise depends on the time window that the signal can be examined over.

The time window in basic loudness memory is about 200 milliseconds. To that extent, we can indeed extract signal from noise. However, we can not do the same level of matched filtering or signal detection that a machine working over many seconds can do.

What's more, we can not narrow the filters in our ears, they are pretty much established as fixed-bandwidth filters. Narrowing filters is another way (it is effectively a limited form of matched filtering) to extract signal from background, but in that sense we are very limited.

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