  We investigate the improvements in Shack-Hartmann wavefront sensor image
processing that can be realised using total variation minimisation techniques
to remove noise from these images. We perform Monte-Carlo simulation to
demonstrate that at certain signal-to-noise levels, sensitivity improvements of
up to one astronomical magnitude can be realised. We also present on-sky
measurements taken with the CANARY adaptive optics system that demonstrate an
improvement in performance when this technique is employed, and show that this
algorithm can be implemented in a real-time control system. We conclude that
total variation minimisation can lead to improvements in sensitivity of up to
one astronomical magnitude when used with adaptive optics systems.
