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Ab dem 13. Juni 2024 knnen interessierte und prfungserfahrene Organisationen die Zulassung als Prfungsstelle zur Durchfhrung von Deutsch-Tests fr den Beruf gem 23 Satz 2 Deutschsprachfrderverordnung (DeuFV) beantragen.
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In single molecule localization-based super-resolution imaging, high labeling density or the desire for greater data collection speed can lead to clusters of overlapping emitter images in the raw super-resolution image data. We describe a Bayesian inference approach to multiple-emitter fitting that uses Reversible Jump Markov Chain Monte Carlo to identify and localize the emitters in dense regions of data. This formalism can take advantage of any prior information, such as emitter intensity and density. The output is both a posterior probability distribution of emitter locations that includes uncertainty in the number of emitters and the background structure, and a set of coordinates and uncertainties from the most probable model.
In single molecule localization microscopy (SMLM) super-resolution approaches1,2,3,4, a sparse subset of single fluorescent emitters that label the target structure is activated and the position of each isolated emitter is found with a precision much better than the diffraction limit. Accumulation of enough label positions allows the reconstruction of images with high spatial resolution5. Dense images with overlapping emitters can be either unavoidable due to densely labeled structures, or desired to shorten data collection time. However, improper analysis of this data can lead to artifacts, such as a contrast inversion in the super-resolution image (dense areas appear sparse)6. One way to ameliorate this issue is to use multiple-emitter fitting approaches6,7,8,9,10,11,12, which allow modeling and/or fitting of multiple overlapping emitters. Several multiple-emitter fitting methods have been reported including approaches based on maximum likelihood6, deconvolution with L1 norm constraints9,10, PSF radial symmetry and intermittency11, using a Bayesian approach to integrate over all possible positions and blinking events of emitters7, and deep learning13,14.
In this work, we describe a BAyesian Multiple-emitter Fitting (BAMF) analysis that uses Reversible Jump Markov Chain Monte Carlo (RJMCMC)15,16. The Bayesian formalism allows the inclusion of strong prior information such as the photophysics of the probe and the emitter density. RJMCMC allows classification uncertainty, i.e., uncertainty in the true number of emitters to be incorporated in the emitter location probability distribution. BAMF also couples background estimation and its uncertainty with inference of emitter locations and intensities. The result is a posterior probability distribution for emitter positions that considers both prior knowledge and sources of uncertainty that are often ignored.
The entire BAMF algorithm consists of several steps (Fig. 1a): (1) converting raw data to photon counts, (2) estimation of the intensity prior, (3) division of each image into subregions, (4) the core RJMCMC algorithm, (5) using the RJMCMC chain to initialize MCMC within the most probable space, (6) using the MCMC chain to calculate the parameters and their associated uncertainties, and (7) making the final reconstructions by removing the localizations in the overlapping areas of the subregions (Supplementary Video 1), and combining the results.
Data flow, jump types and the chain. (a) The data flow. Boxes show stages of the analysis. (b) From left to right, a new spot is detected through a birth event. From right to left, a death event is proposed and an existing emitter is removed. (c) From left to right, an existing emitter splits into two emitters. From right to left, two adjacent emitters merge into a single one. (d) From left to right, photons are taken from N existing emitters to make a new one. Right to left, an existing emitter breaks into N pieces which are added to N nearby emitters. G-split and G-merge stand for generalized split and generalized merge. (e) Left, the plot of a chain of 8,000 jumps, where lighter red shows the burn-in part and the darker red shows the chain after convergence. Right figure depicts the chain after convergence inside the green box. (f) The conversion jump uses the priors on intensities to classify the emitters as either a signal emitter, or an emitter used to model structured background.
The RJMCMC step is used within a fitting subregion and calculates a posterior distribution to make inferences about a set of parameters. This requires both a likelihood model and prior distributions. The likelihood is calculated assuming a model consisting of a set of emitter positions, a PSF model (2D Gaussian6,19 or provided by the user), a tilted plane as unstructured background and Poisson statistics (Methods; PSF model and likelihood). The emitters model both apparent single emitters (signal) or structured background by using a collection of PSF-sized kernels (background) (Supplementary Fig. 5). Each parameter has a corresponding prior distribution that is given in Table 1.
The output of the RJMCMC step is a parameter chain whose histogram can be interpreted as a probability density landscape of the emitters that considers all possible numbers and positions of emitters. For example, a single emitter appears as a blob-shaped feature in the histogram image of the chain of positions (Fig. 1e and Supplementary Video 3), where the width of the blob can be used to calculate the standard error for the position estimation. Combining the chains from all the subregions, we build the posterior image for each time frame and then add up the posteriors over all time frames to obtain the average posterior reconstruction image, which we simply call the posterior image hereafter. To generate a set of positions and uncertainties from the elements of the RJMCMC chain from the most probable model, the Maximum a Posteriori model of Number of emitters (MAPN), is either used directly or used to initialize a MCMC chain for the MAPN model. The results are used to calculate the positions and associated uncertainties. These returned localizations are then used to reconstruct an image. The posterior probability image includes uncertainty over the number of emitters, whereas the MAPN result can provide locations and standard errors that can be used in subsequent analysis (Supplementary Fig. 2).
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