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Significance Single-molecule localization microscopy (SMLM) is quickly becoming an indispensable tool for studying biological structures. Meanwhile, we are presented with new challenges in the analyses of SMLM data arising from their unique noise statistics. In this paper, we solved a fundamental problem with regard to the modeling of SMLM data. Specifically, we established a theoretical connection between a set of experimentally acquired SMLM data and the underlying spatial distribution of fluorescent molecules. Based on this framework, we can extract higher-resolution information that is obscured by the raw data. The same framework also allows us to develop better image alignment algorithms, and thus obtain faster and more accurate results in particle fusion applications.

Single-molecule localization microscopy as nonlinear inverse problem