title: Point-spread function reconstruction in ground-based astronomy by l(1)-l(p) model.
abstract: In ground-based astronomy, images of objects in outer space are acquired via ground-based telescopes. However, the imaging system is generally interfered by atmospheric turbulence, and hence images so acquired are blurred with unknown point-spread function (PSF). To restore the observed images, the wavefront of light at the telescope's aperture is utilized to derive the PSF. A model with the Tikhonov regularization has been proposed to find the high-resolution phase gradients by solving a least-squares system. Here we propose the l(1)-l(p) (p=1, 2) model for reconstructing the phase gradients. This model can provide sharper edges in the gradients while removing noise. The minimization models can easily be solved by the Douglas-Rachford alternating direction method of a multiplier, and the convergence rate is readily established. Numerical results are given to illustrate that the model can give better phase gradients and hence a more accurate PSF. As a result, the restored images are much more accurate when compared to the traditional Tikhonov regularization model.
authors.affiliation: Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, China.
authors.forename: Raymond H
authors.initials: RH
authors.lastname: Chan
authors.forename: Xiaoming
authors.initials: X
authors.lastname: Yuan
authors.forename: Wenxing
authors.initials: W
authors.lastname: Zhang