什么是分辨率？超分辨显微术的统计极小极大检验
What is resolution? A statistical minimax testing perspective on super-resolution microscopy
摘要：
作为一般的经验法则，光学显微镜的分辨率（即辨别物体的能力）主要由其点扩散函数（psf）的半高全宽（FWHM）来描述-模糊密度在其最大值的一半处的直径。经典波动光学表明半高宽和分辨率之间存在线性关系，这也体现在著名的阿贝和瑞利准则中，可以追溯到19世纪末。然而，在过去的二十年中，传统的光学显微镜经历了从微观尺度到纳米尺度的转变。这种分辨率的提高伴随着需要纳入观测（可见光子）的随机性，并挑战了经典的可分辨性观点，正如我们在本文中所论证的那样。相反，我们建议从这样的随机数据获得的分辨率的统计描述。我们对可辨别性的概念是基于统计测试，无论是一个还是两个具有相同总强度的物体。对于泊松测量，我们得到的（极大极小）检测边界上的FWHM的线性依赖，而对于均匀高斯模型的分辨率的依赖是非线性的。因此，在小的物理尺度建模均匀高斯是不够的，虽然往往隐含在许多重建算法假设。相比之下，泊松模型及其方差稳定高斯近似似乎提供了一个统计上合理的描述分辨率在纳米级。我们的理论也适用于其他成像装置，如望远镜。
英文摘要：
As a general rule of thumb the resolution of a light microscope (i.e. the ability to discern objects) is predominantly described by the full width at half maximum (FWHM) of its point spread function (psf)---the diameter of the blurring density at half of its maximum. Classical wave optics suggests a linear relationship between FWHM and resolution also manifested in the well known Abbe and Rayleigh criteria, dating back to the end of 19th century. However, during the last two decades conventional light microscopy has undergone a shift from microscopic scales to nanoscales. This increase in resolution comes with the need to incorporate the random nature of observations (light photons) and challenges the classical view of discernability, as we argue in this paper. Instead, we suggest a statistical description of resolution obtained from such random data. Our notion of discernability is based on statistical testing whether one or two objects with the same total intensity are present. For Poisson measurements we get linear dependence of the (minimax) detection boundary on the FWHM, whereas for a homogeneous Gaussian model the dependence of resolution is nonlinear. Hence, at small physical scales modeling by homogeneous gaussians is inadequate, although often implicitly assumed in many reconstruction algorithms. In contrast, the Poisson model and its variance stabilized Gaussian approximation seem to provide a statistically sound description of resolution at the nanoscale. Our theory is also applicable to other imaging setups, such as telescopes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
