CIF:Small:Developing Theory of Spatiotemporal-Resolution and Spatiotemporal-Localization Algorithms for Single-Molecule Localization Microscopy

单分子定位显微镜（SMLM）克服了长期存在的光衍射障碍，提供超分辨率光学成像，对生物研究产生了重大影响。然而，两个重要的问题仍然存在之前，SMLM可以进一步推进。首先，仍然需要的是一个时空分辨率的理论，它讲述了SMLM系统在空间和时间中分辨分子的固有能力，从而量化SMLM系统的每个部分如何影响时空分辨率的信息理论极限。因此，时空分辨率理论将奠定信息理论的基础，并提供指导，在发展的电光硬件，荧光分子和本地化算法，以推进SMLM。其次，文献中的大多数定位算法仅利用单个数据帧的信息。先进的时空定位算法需要开发，以充分利用数据电影的多个帧的信息，以接近时空分辨率的信息理论极限。先进的时空定位算法可以显著提高时空分辨率，满足生物医学研究对超时空分辨率的需求。时空分辨率理论和时空定位算法的发展将在理论和生物医学研究应用方面对SMLM的跨学科研究产生广泛的影响。在本项目中，首先，提出了一种概念新颖的一维（1D），二维（2D），并且基于数据电影的通用模型的Fisher信息来开发3D空间分辨率。系统参数对时空分辨率的影响以及空间和时间分辨率之间的权衡将被分析和数值研究。将开发和模拟实现数据电影的Fisher信息的无偏高斯信息实现估计器。其次，两种类型的先进的时空定位算法将开发充分利用的空间和时间信息的数据电影。一种是最大电影似然（UGIA-M）算法，它最大化整个数据电影的可能性。另一种是时间相关增强算法，利用嵌入在逐帧局部SMLM图像的时间相关性。这两种类型的算法将通过模拟评估的时空分辨率，使用一个通用的分区为基础的度量驱动的均方根最小距离和均方根误差相对于UGIA-M基准，以及通过比较现有的高性能定位算法从文献。这两种算法将被应用于生物标本的真实的数据集的分析，开发的理论和算法的源代码将被发布在公共资源库中，供社区开放访问。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Single-molecule localization microscopy (SMLM) overcame the longstanding light-diffraction barrier to provide super-resolution optical imaging, significantly impacting biological research. Nevertheless, two important problems remain before SMLM can be advanced further. First, still needed is a theory of spatiotemporal resolution which speaks to the inherent power of an SMLM system in resolving a molecule in space and time, thereby quantifying how each part of an SMLM system affects the information-theoretical limit of spatiotemporal resolution. Thus, a spatiotemporal resolution theory would lay an information-theoretic foundation and provide guidance in the development of electro-optical hardware, fluorescence molecules, and localization algorithms to advance SMLM. Second, the majority of localization algorithms in literature exploit the information of only a single data frame. Advanced spatiotemporal localization algorithms need to be developed to fully exploit the information of the multiple frames of a data movie in order to approach the information-theoretic limit of spatiotemporal resolution. Advanced spatiotemporal localization algorithms can significantly enhance spatiotemporal resolution and fulfill the needs of both super spatial and temporal resolutions in biomedical research. The spatiotemporal resolution theory and spatiotemporal location algorithms to be developed in this project will broadly impact interdisciplinary research of SMLM in both theory as well as in applications to biomedical research.In this project, first, a conceptually novel theory of spatiotemporal resolution with respect to one-dimensional (1D), 2D, and 3D spatial resolutions will be developed based on the Fisher information of a universal model of a data movie. The effect of system parameters on the spatiotemporal resolution and the tradeoff between spatial and temporal resolutions will be analytically and numerically investigated. The unbiased Gaussian information-achieving estimator that achieves the Fisher information of a data movie will be developed and simulated. Second, two types of advanced spatiotemporal localization algorithms will be developed to fully exploit the spatial and temporal information in a data movie. One is the maximum movie-likelihood (UGIA-M) algorithm that maximizes the likelihood of an entire data movie. The other is the temporal correlation-enhancement algorithms that exploit the temporal correlation embedded in the frame-by-frame localized SMLM images. The two types of algorithms will be evaluated via simulation in terms of spatiotemporal resolution using a universal partition-based metric driven by root-mean-square minimum distance and root-mean-square error with respect to a UGIA-M benchmark as well as by comparison to existing high-performance localization algorithms from the literature. The two types of algorithms will be applied to the analysis of real datasets of biological specimens, and source code for the developed theory and algorithms will be posted in public repositories for open access by the community.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.