Lucky imaging is a high-angular-resolution astronomical image reconstruction technique which can effectively reduce or remove the effects of atmospheric turbulence. There have been successful real-time lucky imaging algorithms and corresponding implementations in the spatial domain. Although the results of lucky imaging algorithms in the frequency domain are better than in the spatial domain, until now there has been no corresponding real-time algorithm and implementation due to its complexity. This paper proposes a real-time lucky imaging algorithm based on Fourier transform that features real-time processing and dynamic updating and display. The algorithm is implemented on a small- or medium-scale field programmable gate array (FPGA) development board. In this system, a two-dimensional fast Fourier transform of the image is carried out by means of dimension reduction. In order to achieve real-time lucky imaging in the frequency domain, the sum of the squares of the real and imaginary parts are used to replace the amplitude for data selection, and the method of image grouping is used to speed up the data selection. Compared with other real-time lucky imaging algorithms in the spatial domain, this algorithm shows great advantages in image quality. Moreover, the system can carry out real-time lucky imaging processing in the frequency domain for more than 10000 frames of an original image of 512 × 512 pixels continuously, and dynamic display with an image of 128 × 128 pixels. The experimental results illustrate the validity of the proposed algorithm and the feasibility of the proposed implementation techniques for the FPGA-based algorithm.

中文翻译：

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基于傅里叶变换的实时幸运成像算法及其实现技术

幸运成像是一种高角分辨率的天文图像重建技术，可以有效减少或消除大气湍流的影响。在空间领域已经有成功的实时幸运成像算法和相应的实现。虽然幸运成像算法在频域的结果比在空间域的要好，但由于其复杂性，直到现在还没有相应的实时算法和实现。本文提出了一种基于傅里叶变换的实时幸运成像算法，具有实时处理和动态更新显示的特点。该算法在中小型现场可编程门阵列 (FPGA) 开发板上实现。在这个系统中，通过降维的方式对图像进行二维快速傅里叶变换。为了实现频域的实时幸运成像，采用实部和虚部的平方和代替幅度进行数据选择，采用图像分组的方法加快数据选择。与空间域的其他实时幸运成像算法相比，该算法在图像质量上表现出很大的优势。并且，该系统可以连续对10000多帧512×512像素的原始图像进行频域实时幸运成像处理，动态显示128×128像素的图像。