a single supply headphone amplifier (top) with a noise cancellation circuit (bot).
the circuit could be driven by an 3V Li battery or two 1.5 V normal batterys.
the bottom circuit is an allpass filter used to invert the input which is than added to the output.
In real application a delay circuit would lead to better cancellation (you have to put your signal in the right phase to the noise).
This circuit could be used in DIY Headphones.