多共轭自适应光学中的小波方法
Wavelet methods in multi-conjugate adaptive optics
AI总结：
针对多共轭自适应光学中的大气层析成像问题，提出一种基于紧支撑小波局部性质的重建方法，通过贝叶斯MAP估计和共轭梯度算法实现快速稳定重建，并在欧洲南方天文台的OCTOPUS仿真工具上验证了性能。
摘要：
下一代地面望远镜严重依赖自适应光学来克服大气湍流的限制。在未来的自适应光学模式中，如多共轭自适应光学（MCAO），大气层析成像是主要的数学和计算挑战。在这个严重不适定问题中，需要一个快速且稳定的重建算法，能够考虑望远镜成像的许多实际现象。我们提出了一种用于大气层析成像问题的新重建方法，并在MCAO背景下展示了其性能和灵活性。我们的方法基于使用紧支撑小波的局部性质，无论是在空间域还是频率域。大气层析成像问题的重建是通过求解贝叶斯MAP估计器，使用基于共轭梯度的算法获得的。还引入了一种带预处理的加速算法。数值性能在欧洲南方天文台的官方端到端仿真工具OCTOPUS上得到了展示。
英文摘要：
The next generation ground-based telescopes rely heavily on adaptive optics for overcoming the limitation of atmospheric turbulence. In the future adaptive optics modalities, like multi-conjugate adaptive optics (MCAO), atmospheric tomography is the major mathematical and computational challenge. In this severely ill-posed problem a fast and stable reconstruction algorithm is needed that can take into account many real-life phenomena of telescope imaging. We introduce a novel reconstruction method for the atmospheric tomography problem and demonstrate its performance and flexibility in the context of MCAO. Our method is based on using locality properties of compactly supported wavelets, both in the spatial and frequency domain. The reconstruction in the atmospheric tomography problem is obtained by solving the Bayesian MAP estimator with a conjugate gradient based algorithm. An accelerated algorithm with preconditioning is also introduced. Numerical performance is demonstrated on the official end-to-end simulation tool OCTOPUS of European Southern Observatory.
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