Ground-based astronomy refers to acquiring images of objects in outer
space via ground-based telescopes. Because of atmospheric turbulence,
images so acquired are blurry. One way to estimate the unknown blur or
point spread function (PSF) is by using natural or artificial guide
stars. Once the PSF is known, the images can be deblurred using
well-known deblurring methods. Another way to estimate the PSF is to
make use the aberration of wavefronts received at the telescope, i.e.,
the phase, to derive the PSF. However, the phase is not readily
available; instead only its low-resolution gradients can be collected
by wavefront sensors. In this talk, we will discuss how to use
regularization methods to reconstruct high-resolution phase gradients
and then use them to recover the phase and then the PSF in high
accuracy. Our model can be solved efficiently by alternating direction
method of multiplier whose convergence has been well established.
Numerical results will be given to illustrate that our new model is
efficient and give more accurate estimation for the PSF.