SIAM Journal on Imaging Sciences, Volume 13, Issue 2, Page 775-806, January 2020.
Adaptive optics is a commonly used technique to correct the phase distortions caused by the Earth's atmosphere to improve the image quality of the ground-based imaging systems. However, the observed images still suffer from the blur caused by the adaptive optics residual wavefront. In this paper, we propose a model for reconstructing the residual phase in high resolution from a sequence of deformable mirror data. Our model is based on the turbulence statistics and the Taylor frozen flow hypothesis with knowledge of the wind velocities in atmospheric turbulence layers. A tomography problem for the phase distortions from different altitudes is solved in order to get a high quality phase reconstruction. We also consider inexact tomography operators resulting from the uncertainty in the wind velocities. The wind velocities are estimated from the deformable mirror data and, additionally, by including them as unknowns in the objective function. We provide a theoretical analysis on the existence of a minimizer of the objective function. To solve the associated joint optimization problem, we use an alternating minimization method which results in a high resolution reconstruction algorithm with adaptive wind velocities. Numerical simulations are carried out to show the effectiveness of our approach.

中文翻译：

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闭环自适应光学系统中高分辨率相位的重建

SIAM影像科学杂志，第13卷，第2期，第775-806页，2020年1月。
自适应光学是一种常用技术，可以纠正由地球大气层引起的相位畸变，从而改善基于地面的成像系统的图像质量。然而，观察到的图像仍然遭受由自适应光学残余波前引起的模糊。在本文中，我们提出了一个用于从一系列可变形镜像数据中高分辨率重建残差相位的模型。我们的模型基于湍流统计数据和泰勒冻结流假设，并了解了大气湍流层中的风速。解决了来自不同高度的相位畸变的层析成像问题，以便获得高质量的相位重建。我们还考虑了由于风速的不确定性而导致的不精确的层析成像操作者。风速是根据可变形镜面数据估算的，此外，还可以将风速作为未知数包含在目标函数中。我们提供关于目标函数的极小值的存在的理论分析。为了解决相关联的联合优化问题，我们使用一种交替最小化方法，该方法导致了具有自适应风速的高分辨率重建算法。进行了数值模拟以显示我们方法的有效性。我们使用一种交替最小化方法，从而产生具有自适应风速的高分辨率重建算法。进行了数值模拟以显示我们方法的有效性。我们使用一种交替最小化方法，从而产生具有自适应风速的高分辨率重建算法。进行了数值模拟以显示我们方法的有效性。