Fisher information theory for parameter estimation in single molecule microscopy: tutorial.
Fisher information theory for parameter estimation in single molecule microscopy: tutorial.
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DOI：
10.1364/josaa.33.000b36
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发表时间：
2016-07-01
期刊：
影响因子：
--
通讯作者：
Ober RJ
中科院分区：
文献类型：
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作者：
Chao J;Sally Ward E;Ober RJ
从图像数据中估计感兴趣的参数代表了在单分子显微镜数据分析中通常执行的任务。例如，根据分子的图像确定分子的位置坐标，构成了标准应用的基础，例如单分子跟踪和基于定位的超分辨率图像重建。假设所用的估计器平均恢复，那么参数的真值、其精度或标准差至多等于Cramér-Rao下限的平方根。因此，Cramér-Rao下限可以用作评估估计器精度的基准。此外，由于它的值可以针对不同的实验设置进行计算和评估，因此它是一种有用的实验设计工具。本教程演示了一个专门为计算单分子显微镜和更广泛的荧光显微镜中估计问题的Cramér-Rao下限而开发的数学框架。该材料包括作为所有图像数据基础的光子检测过程的介绍、描述用不同探测器类型获取的图像的各种图像数据模型、以及计算下限所需的费舍尔信息表达式。在整个教程中，涉及具体估计问题的例子被用来说明各种因素对参数估计精度的影响，更广泛地说，是为了展示数学框架的灵活性。
Estimation of a parameter of interest from image data represents a task that is commonly carried out in single molecule microscopy data analysis. The determination of the positional coordinates of a molecule from its image, for example, forms the basis of standard applications such as single molecule tracking and localization-based superresolution image reconstruction. Assuming that the estimator used recovers, on average, the true value of the parameter, its accuracy, or standard deviation, is then at best equal to the square root of the Cramér-Rao lower bound. The Cramér-Rao lower bound can therefore be used as a benchmark in the evaluation of the accuracy of an estimator. Additionally, as its value can be computed and assessed for different experimental settings, it is useful as an experimental design tool. This tutorial demonstrates a mathematical framework that has been specifically developed to calculate the Cramér-Rao lower bound for estimation problems in single molecule microscopy and, more broadly, fluorescence microscopy. The material includes a presentation of the photon detection process that underlies all image data, various image data models that describe images acquired with different detector types, and Fisher information expressions that are necessary for the calculation of the lower bound. Throughout the tutorial, examples involving concrete estimation problems are used to illustrate the effects of various factors on the accuracy of parameter estimation, and more generally, to demonstrate the flexibility of the mathematical framework.