I can understand how bipolar (or single differential) EMG reduces noise by cancelling the signal that is common to both inputs. How does double differential EMG further optimize this?
The double differential uses three electrodes that are placed in series with the muscle. The idea is that it can pick up a bigger area and minimize the crosstalk. It also acts as a highpass, discarding low-frequency waves that usually come from external sources (non-emg). This paper compares different configurations and discusses the double differential.
Article Evaluation of methods to minimize cross talk in surface elec...
There are three common types of noise: white noise, flicker noise and thermal noise.
What types of noise do you want to reduce? If you can write the small signal model of the double differential amplifiers, the noise can be analyzed easier!