Picking out a signal that appears to be noise inside a large signal I have a signal from a photodiode sensor that has two types of noise. One type of noise is ambient light white noise that gets introduced just from the surrounding environemnt. The other type of noise is due to the motion of the sensor.

Currently i don't seem to have a problem filtering out the white noise when the sensor is held still. But when the sensor is moving i get very large noise from motion, this noise is much larger than the signal i am interested in and as a result makes the signal I want look like noise.

The signal i am interested is anywhere between 0.75Hz and 4Hz, the motion signal can be anywhere from 0.25Hz to 5Hz. 

I am currently using a butterworth filter between 0.5 and 4 Hz and then a moving average to smooth it out. But this causes the signal to be lost in the motion noise.

I have looked into adaptive filters but am not sure whether i should try to implement them or not because i do not have enough experience with them to tell whether they will help my problem or not.

Are there techniques that are used to pick out signals that share frequency with noise?
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.