Picking out a signal that appears to be noise inside a large signal
Adaptive filters could be used in situations where you have a reference signal, what adaptive filters basically do is to try modelling the signal that is present in captured signal using reference signal. So, we can subtract and/or extract the required signal.

In the situation mentioned in question, you can use adaptive filter if you have reference for either the signal you are interested in or the noise you want to remove. If you have the noise signal as reference adaptive filters will remove the required signal(signal of interest) from input and only noise will be remaining, now this noise can be subtracted from original input signal to get the required signal(signal of interest).        

Same could be done if signal of interest is present as a reference, but in this case the adaptive filters output will be the required output.