Point-spread function reconstruction in ground-based astronomy by l <sup>1</sup>-l<sup>p</sup> 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 < sup > 1 < /sup > -l < sup > p < /sup > (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. © 2012 Optical Society of America 1084-7529/12/112263-09$15.00/0.