  The Shack-Hartmann wavefront sensor is widely used to measure aberrations
induced by atmospheric turbulence in adaptive optics systems. However if there
exists strong atmospheric turbulence or the brightness of guide stars is low,
the accuracy of wavefront measurements will be affected. In this paper, we
propose a compressive Shack-Hartmann wavefront sensing method. Instead of
reconstructing wavefronts with slope measurements of all sub-apertures, our
method reconstructs wavefronts with slope measurements of sub-apertures which
have spot images with high signal to noise ratio. Besides, we further propose
to use a deep neural network to accelerate wavefront reconstruction speed.
During the training stage of the deep neural network, we propose to add a
drop-out layer to simulate the compressive sensing process, which could
increase development speed of our method. After training, the compressive
Shack-Hartmann wavefront sensing method can reconstruct wavefronts in high
spatial resolution with slope measurements from only a small amount of
sub-apertures. We integrate the straightforward compressive Shack-Hartmann
wavefront sensing method with image deconvolution algorithm to develop a
high-order image restoration method. We use images restored by the high-order
image restoration method to test the performance of our the compressive
Shack-Hartmann wavefront sensing method. The results show that our method can
improve the accuracy of wavefront measurements and is suitable for real-time
applications.
