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 l1-lp (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.
Original language | English |
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Pages (from-to) | 2263-2271 |
Number of pages | 9 |
Journal | Journal of the Optical Society of America A: Optics and Image Science, and Vision |
Volume | 29 |
Issue number | 11 |
Early online date | 9 Oct 2012 |
DOIs | |
Publication status | Published - Nov 2012 |
Externally published | Yes |
Funding
The first author is supported in part by Hong Kong Research Grants Council (HKRGC) Grant No. CUHK400510 and CUHK Direct Allocation Grant 2060408, and the second author is supported by HKRGC Grant No. HKBU203311.