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，提供了超分辨率光学成像，对生物学研究产生了重大影响。然而，在SMLM进一步发展之前，仍然存在两个重要问题。首先，仍然需要一个时空分辨率理论，该理论说明了SMLM系统在空间和时间上解析分子的固有能力，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，时空分辨率理论将为电光硬件、荧光分子和定位算法的发展奠定信息论基础，并为SMLM的发展提供指导。其次，文献中的大多数定位算法仅利用单个数据帧的信息。为了达到时空分辨率的信息论极限，需要开发先进的时空定位算法，以充分利用数据电影的多帧信息。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和超时空分辨率的需求。本项目将开发的时空分辨率理论和时空定位算法将对SMLM的跨学科研究产生广泛的理论影响，并在生物医学研究中应用。在本项目中，首先，将基于数据电影通用模型的Fisher信息，开发一维（1D）、二维和三维空间分辨率的时空分辨率概念新理论。系统参数对时空分辨率的影响以及时空分辨率和时间分辨率之间的权衡将进行分析和数值研究。开发并仿真了能获得数据电影Fisher信息的无偏高斯信息实现估计器。其次，开发两种先进的时空定位算法，以充分利用数据电影中的时空信息。一种是最大电影可能性（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，它利用嵌入在逐帧定位的SMLM图像中的时间相关性。这两种类型的算法将通过模拟在时空分辨率方面进行评估，使用基于通用分区的度量，该度量由相对于UGIA-M基准的均方根最小距离和均方根误差驱动，并与文献中现有的高性能定位算法进行比较。这两种算法将应用于分析生物标本的真实数据集，并将开发的理论和算法的源代码发布在公共存储库中，供社区开放获取。该奖项反映了美国国家科学基金会的法定使命，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.