Because of atmospheric turbulence, images of objects in outer space acquired via ground-based telescopes are usually blurry.

One way to estimate the blurring kernel or point spread function (PSF) is to make use of the aberration of wavefronts received at the telescope, i.e., the phase. However only the low-resolution wavefront gradients can be collected by wavefront sensors.

In this talk, I will introduce the necessary background first and then discuss how to use regularization methods to reconstruct high-resolution phase gradients and then use them to recover the phase and the PSF in high accuracy.