Abstract
A data movie of stochastic optical localization nanoscopy contains spatial and temporal correlations, both providing information of emitter locations. The majority of localization algorithms in the literature estimate emitter locations by frame-by-frame localization (FFL), which exploit only the spatial correlation and leave the temporal correlation into the FFL nanoscopy images. The temporal correlation contained in the FFL images, if exploited, can improve the localization accuracy and the image quality. In this paper, we analyze the properties of the FFL images in terms of root mean square minimum distance (RMSMD) and root mean square error (RMSE). It is shown that RMSMD and RMSE can be potentially reduced by a maximum fold equal to the square root of the average number of activations per emitter. Analyzed and revealed are also several statistical properties of RMSMD and RMSE and their relationship with respect to a large number of data frames, bias and variance of localization errors, small localization errors, sample drift, and the worst FFL image. Numerical examples are taken and the results confirm the prediction of analysis. The ideas about how to develop an algorithm to exploit the temporal correlation of FFL images are also briefly discussed. The results suggest development of two kinds of localization algorithms: the algorithms that can exploit the temporal correlation of FFL images and the unbiased localization algorithms.
Highlights
A data movie of stochastic optical localization nanoscopy contains spatial and temporal correlations, both providing information of emitter locations
These results suggest that in order to achieve a high quality of localization nanoscopy images it is important to develop two kinds of algorithms: the algorithms that can exploit temporal correlation contained in frame-by-frame localization (FFL) images and the unbiased localization algorithms
We present a numerical example to demonstrate the properties of root mean square minimum distance (RMSMD) for the FFL images
Summary
A data movie of stochastic optical localization nanoscopy contains spatial and temporal correlations, both providing information of emitter locations. If the spatial and temporal correlations are jointly and optimally exploited in localization of emitters, the localization accuracy can approach the bound that the data movie can provide Such an advanced localization algorithm is usually computationally complicated; and this is probably the reason why the majority of localization algorithms estimate emitter locations frame by frame independently. The temporal correlation is still contained in the FFL image, which if exploited, shall improve the localization accuracy of estimated emitter locations and the quality of nanoscopy image as well. It is found that while an FFL image is random, its RMSMD converges to a deterministic constant as the average number of activations per emitter tends to infinity This implies that for a sufficiently large , increasing the number of acquired data frames improves little the quality of an FFL image in terms of reduction of RMSMD variation. The ideas about how to develop an algorithm to exploit the temporal correlation of Scientific Reports | (2020) 10:11844 |
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
