Analyzing point spread functions for multiple emitter fitting by posterior density estimation
R. van Dijk (TU Delft - Mechanical Engineering)
C.S. Smith – Mentor (TU Delft - Team Carlas Smith)
J.P. Cnossen – Mentor (TU Delft - Team Carlas Smith)
B. De Schutter – Coach (TU Delft - Team Bart De Schutter)
K.S. Grußmayer – Coach (TU Delft - BN/Kristin Grussmayer Lab)
S. Caneva – Coach (TU Delft - Dynamics of Micro and Nano Systems)
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Github link to the algorithm
https://github.com/qnano/rjmcmc3DGoogle collab algorithm demonstration using a Gaussian fit astigmatic PSF
https://colab.research.google.com/github/qnano/rjmcmc3D/blob/master/colab_example.ipynb#scrollTo=bWMSbYWZUUSuGoogle collab algorithm demonstration using c-spline astigmatic PSF
https://colab.research.google.com/github/qnano/rjmcmc3D/blob/master/colab_example_cspline.ipynb#scrollTo=P4IK4ue7r9rbOther than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
The microscope is an essential tool for biologists. Since the late 16th century, it has given researchers a better understanding of cell processes and greatly advanced healthcare. In this century, Single molecule localization microscopy (SMLM) has revolutionized optical microscopy by breaking the optical diffraction limit. Sparsely activating emitters in a sample labeled with fluorophores, the object can be reconstructed by estimating their positions using the system point spread function (PSF). These localization algorithms are the state of the art
in optical imaging, using unbiased estimators to reach the theoretical minimum uncertainty, or Cramér-Rao lower bound (CRLB).
While SMLM works well when emitters are sparsely activated, overlap of the emitter images is inevitable for thick or densely labeled samples. When SMLM is used on such images, the estimates become biased and the algorithm cannot find the correct number of emitters. Most techniques also make a deterministic estimate and are incapable of representing the uncertainty of estimates for dense samples.
A three-dimensional, Bayesian multiple emitter fitting algorithm is constructed using reversible jump Markov chain Monte Carlo (RJMCMC). While following the structure of Bayesian multiple-emitter fitting (BAMF), novel RJMCMC moves are designed to sample the parameters. The algorithm also jumps through models, estimating the number of emitters. It asymptotically samples from the posterior, revealing uncertainties in three-dimensional imaging that other techniques are incapable of imaging.
The algorithm was tested with astigmatic and biplane imaging. It has proven capable of consistently finding the correct model when a prior on emitter intensity is used. When separating two emitters, posterior density reconstruction revealed non-Gaussian emitter position uncertainties. Upon further investigation, the posterior density was found to be multimodal, with
both modes representative of the data and indistinguishable in terms of likelihood. This shows the algorithm can quantify three-dimensional PSF degeneracy and can become a vital tool for researchers to analyze their imaging setup. We also expect it to be especially effective when combined with modulation-enhanced localization microscopy (meLM) techniques.