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.
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