What is resolution? A statistical minimax testing perspective on superresolution microscopy

Kulaitis, Gytis; Munk, Axel; Werner, Frank

doi:10.1214/20-aos2037

Cited by 7 publications

(4 citation statements)

References 58 publications

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“…From a statistical perspective, the recovery of spatial intensity and specimen distribution from super-resolution fluorescence microscopy images leads to sophisticated convolution models with Poisson or Binomial data distributions, which in themselves present a number of challenges (see, e.g. [9][10][11][12] and references therein).…”

Section: Super-resolution Microscopymentioning

confidence: 99%

“…An often used measure describing the shape of h and also of the microscope's resolution is its full width at half maximum (FWHM), cf. Kulaitis et al [12] for an explanation in statistical terms. In the case of a Gaussian peak PSF h with variance 𝜎 2 , one has FWHM = 2√2 log 2𝜎.…”

Section: Modeling Notation and Prerequisitesmentioning

confidence: 99%

“…For this, we pose the following physical assumption: Assumption 3. The brightness within the region R is approximately constant if R is sufficiently small and the functions H l defined in (12) do not depend on k.…”

Section: Statistical Molecule Countingmentioning

confidence: 99%

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Toward quantitative super-resolution microscopy: molecular maps with statistical guarantees

Proksch,

Werner,

Keller–Findeisen

et al. 2023

Microscopy

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Quantifying the number of molecules from fluorescence microscopy measurements is an important topic in cell biology and medical research. In this work, we present a consecutive algorithm for super-resolution (stimulated emission depletion (STED)) scanning microscopy that provides molecule counts in automatically generated image segments and offers statistical guarantees in form of asymptotic confidence intervals. To this end, we first apply a multiscale scanning procedure on STED microscopy measurements of the sample to obtain a system of significant regions, each of which contains at least one molecule with prescribed uniform probability. This system of regions will typically be highly redundant and consists of rectangular building blocks. To choose an informative but non-redundant subset of more naturally shaped regions, we hybridize our system with the result of a generic segmentation algorithm. The diameter of the segments can be of the order of the resolution of the microscope. Using multiple photon coincidence measurements of the same sample in confocal mode, we are then able to estimate the brightness and number of molecules and give uniform confidence intervals on the molecule counts for each previously constructed segment. In other words, we establish a so-called molecular map with uniform error control. The performance of the algorithm is investigated on simulated and real data.

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Section: Super-resolution Microscopymentioning

confidence: 99%

Section: Modeling Notation and Prerequisitesmentioning

confidence: 99%

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Toward quantitative super-resolution microscopy: molecular maps with statistical guarantees

Proksch,

Werner,

Keller–Findeisen

et al. 2023

Microscopy

Self Cite

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show abstract

“…chemically attached to each protein within a complex protein ensemble and then are excited with a laser beam. The resulting, emitted photons indicate the spatial position of the objects of interest in the proper experimental setup [Kulaitis et al, 2021]. However, the marker has a limited labelling efficiency s x ∈ (0, 1] at each location x ∈ X and we only observe a location which has been labelled by the marker and finally emits photons.…”

Section: Bernoulli Modelmentioning

confidence: 99%

Unbalanced Kantorovich-Rubinstein distance and barycenter for finitely supported measures: A statistical perspective

Heinemann¹,

Klatt²,

Munk³

2022

Preprint

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We propose and investigate several statistical models and corresponding sampling schemes for data analysis based on unbalanced optimal transport (UOT) between finitely supported measures. Specifically, we analyse Kantorovich-Rubinstein (KR) distances with penalty parameter C > 0. The main result provides non-asymptotic bounds on the expected error for the empirical KR distance as well as for its barycenters. The impact of the penalty parameter C is studied in detail. Our approach justifies randomised computational schemes for UOT which can be used for fast approximate computations in combination with any exact solver. Using synthetic and real datasets, we empirically analyse the behaviour of the expected errors in simulation studies and illustrate the validity of our theoretical bounds.

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A Minimax Testing Perspective on Spatial Statistical Resolution in Microscopy

Kulaitis

Munk

Werner

2023

Springer Proceedings in Mathematics &Amp; Statistics

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What is resolution? A statistical minimax testing perspective on superresolution microscopy

Cited by 7 publications

References 58 publications

Toward quantitative super-resolution microscopy: molecular maps with statistical guarantees

Toward quantitative super-resolution microscopy: molecular maps with statistical guarantees

Unbalanced Kantorovich-Rubinstein distance and barycenter for finitely supported measures: A statistical perspective

A Minimax Testing Perspective on Spatial Statistical Resolution in Microscopy

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