Abstract
We present a fast and model-free 2D and 3D single-molecule localization algorithm that allows more than 3 × 106 localizations per second to be calculated on a standard multi-core central processing unit with localization accuracies in line with the most accurate algorithms currently available. Our algorithm converts the region of interest around a point spread function to two phase vectors (phasors) by calculating the first Fourier coefficients in both the x- and y-direction. The angles of these phasors are used to localize the center of the single fluorescent emitter, and the ratio of the magnitudes of the two phasors is a measure for astigmatism, which can be used to obtain depth information (z-direction). Our approach can be used both as a stand-alone algorithm for maximizing localization speed and as a first estimator for more time consuming iterative algorithms.
Highlights
Single-molecule localization microscopy (SMLM) has become a widely used technique in the biomolecular sciences since seminal contributions successfully demonstrated a roughly ten-fold improvement in spatial resolution over conventional fluorescence microscopy.1–3 The key concept of SMLM is that the position of a single fluorescent emitter can be determined with an accuracy exceeding the diffraction limit as long as the emission of different molecules is sufficiently separated in time and space.4–6 To localize the individual particles with sub-diffraction accuracy in two or three dimensions, a number of approaches have been developed.7 Frequently employed localization algorithms involve the use of two-dimensional Gaussian functions to fit the intensity profile of individual emitters with high precision
In terms of localization speed, pSMLM-3D achieved more than 3 × 106 localizations per second (3 MHz) when using regions of interests (ROIs) with 7 × 7 pixels [Fig. 2(a)]
This localization rate is at least an order of magnitude faster than our adapted implementations of other central processing unit (CPU)-based algorithms and even significantly faster than GPU-enabled Gauss-MLE
Summary
Single-molecule localization microscopy (SMLM) has become a widely used technique in the biomolecular sciences since seminal contributions successfully demonstrated a roughly ten-fold improvement in spatial resolution over conventional fluorescence microscopy. The key concept of SMLM is that the position of a single fluorescent emitter can be determined with an accuracy exceeding the diffraction limit as long as the emission of different molecules is sufficiently separated in time and space. To localize the individual particles with sub-diffraction accuracy in two or three dimensions, a number of approaches have been developed. Frequently employed localization algorithms involve the use of two-dimensional Gaussian functions to fit the intensity profile of individual emitters with high precision. Single-molecule localization microscopy (SMLM) has become a widely used technique in the biomolecular sciences since seminal contributions successfully demonstrated a roughly ten-fold improvement in spatial resolution over conventional fluorescence microscopy.. The key concept of SMLM is that the position of a single fluorescent emitter can be determined with an accuracy exceeding the diffraction limit as long as the emission of different molecules is sufficiently separated in time and space.. Employed localization algorithms involve the use of two-dimensional Gaussian functions to fit the intensity profile of individual emitters with high precision. These approaches, tend to be slow due to their iterative nature, albeit data analysis in real time using graphics processing units (GPUs) has been successfully demonstrated..
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