  Point-wise localization of individual fluorophores is a critical step in
super-resolution microscopy and single particle tracking. Although the methods
are limited by the accuracy in localizing individual flourophores, this
point-wise accuracy has so far only been estimated by theoretical best case
approximations, disregarding for example motional blur, out of focus broadening
of the point spread function and time varying changes in the fluorescence
background. Here, we show that pointwise localization uncertainty can be
accurately estimated directly from imaging data using a Laplace approximation
constrained by simple mircoscope properties. We further demonstrate that the
estimated localization uncertainty can be used to improve downstream
quantitative analysis, such as estimation of diffusion constants and detection
of changes in molecular motion patterns. Most importantly, the accuracy of
actual point localizations in live cell super-resolution microscopy can be
improved beyond the information theoretic lower bound for localization errors
in individual images, by modeling the fluorophores' movement and accounting for
their point-wise localization uncertainty.
