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Bayesian posterior density estimation reveals degeneracy in three-dimensional multiple emitter localization.

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A new Bayesian algorithm improves 3D single-molecule localization microscopy by accurately fitting overlapping emitters. This method reduces uncertainty and enhances model estimation for dense samples, advancing super-resolution imaging techniques.

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Area of Science:

  • * Biophysics
  • * Optical Microscopy
  • * Computational Biology

Background:

  • * Single-molecule localization microscopy (SMLM) relies on sparse emitter activation to overcome diffraction limits.
  • * Overlapping emitter images in dense or thick samples lead to biased parameter estimates and incorrect emitter counts in standard SMLM.
  • * Existing multiple emitter fitting methods struggle with point spread function (PSF) degeneracy, causing model and parameter uncertainty.

Purpose of the Study:

  • * To develop a robust 3D Bayesian algorithm for fitting multiple, overlapping emitters in SMLM.
  • * To accurately estimate emitter parameters (3D position, photon intensity) and associated uncertainties.
  • * To evaluate the performance of different 3D imaging techniques for multiple emitter fitting.

Main Methods:

  • * Developed a 3D Bayesian multiple emitter fitting algorithm utilizing Reversible Jump Markov Chain Monte Carlo (RJMCMC).
  • * The algorithm reconstructs the posterior probability distribution of both the model (number of emitters) and parameters.
  • * Evaluated algorithm performance by analyzing emitter separation capabilities using astigmatic and biplane PSF imaging.

Main Results:

  • * Astigmatic imaging showed multimodal posterior distributions for emitter positions within 2x the in-focus standard deviation of the PSF, indicating positional ambiguity.
  • * Biplane imaging successfully separated emitters up to 0.75x the in-focus standard deviation of the PSF without multimodality.
  • * The algorithm effectively identified PSF degeneracy and quantified imaging technique performance.

Conclusions:

  • * The developed 3D Bayesian algorithm accurately estimates parameters and uncertainties for overlapping emitters in SMLM.
  • * Multimodality in posterior distributions serves as an indicator of PSF degeneracy and localization ambiguity.
  • * Biplane imaging demonstrates superior performance for 3D multiple emitter fitting compared to astigmatic imaging in certain regimes.