从一幅模糊图像中提取单分子或重叠分子内部的超分辨结构
Extracting Super-resolution Structures inside a Single Molecule or Overlapped Molecules from One Blurred Image
摘要：
在一些超分辨率技术中，相邻点在不同时间被照亮。因此，即使图像由于衍射而非常模糊，也可以检测它们的位置和光强度。根据传统的理论，由于衍射极限的存在，图像中的高频成分被去除，无法恢复点的内部细节。但本研究发现了一个例外，衍射模糊图像可以提取完整的信息。在这样的“可分辨条件”下，轮廓和细节信息都不会被衍射破坏。因此，它可以通过在空间域或频率域求解方程组可逆地恢复。这个条件与现有超分辨技术的成像条件密切相关。在此基础上，提出了一种原则上可以实现无限高分辨率的方法，并通过理论分析和仿真实验验证了该方法的有效性。它也可以在感兴趣区域之外没有任何观察到的图像的情况下工作。仿真实验也表明了该算法对一定噪声水平的容忍能力。
英文摘要：
In some super-resolution techniques, adjacent points are illuminated at different times. Thereby, their locations and light intensities can be detected even if the images are very blurred due to diffraction. According to conventional theories, the points' inner details cannot be recovered because the images' high frequency components are removed due to the diffraction-limit. But this study finds an exception, and full information can be extracted from a diffraction-blurred image. In such a "resolvable condition", neither profile nor detail information is damaged by diffraction. Thereby, it can be recovered reversibly by solving equation systems in spatial domain or frequency domain. This condition is tightly relevant to the imaging condition of existing super-resolution techniques. Based on the condition, a method is proposed which can achieve unlimited high resolutions in principle, and its effectiveness is demonstrated by both theoretical analysis and simulation experiments. It can also work without any observed image outside the region of interest. Simulation experiments also show its tolerance to certain level of noise.
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