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 the alternating direction method of multipliers 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.