Statistical Foundations of Nanoscale Photonic Imaging

Munk, Axel; Staudt, Thomas; Werner, Frank

doi:10.1007/978-3-030-34413-9_4

Cited by 9 publications

(10 citation statements)

References 20 publications

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“…It is often derived in the setting of continuous illumination, but the Poisson model can also be motivated by means of the law of small numbers, see e.g. [47].…”

Section: Statistical Modelmentioning

confidence: 99%

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What is resolution? A statistical minimax testing perspective on super-resolution microscopy

Kulaitis¹,

Munk²,

Werner³

2020

Preprint

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As a general rule of thumb the resolution of a light microscope (i.e. the ability to discern objects) is predominantly described by the full width at half maximum (FWHM) of its point spread function (psf)-the diameter of the blurring density at half of its maximum. Classical wave optics suggests a linear relationship between FWHM and resolution also manifested in the well known Abbe and Rayleigh criteria, dating back to the end of 19th century. However, during the last two decades conventional light microscopy has undergone a shift from microscopic scales to nanoscales. This increase in resolution comes with the need to incorporate the random nature of observations (light photons) and challenges the classical view of discernability, as we argue in this paper. Instead, we suggest a statistical description of resolution obtained from such random data. Our notion of discernability is based on statistical testing whether one or two objects with the same total intensity are present. For Poisson measurements we get linear dependence of the (minimax) detection boundary on the FWHM, whereas for a homogeneous Gaussian model the dependence of resolution is nonlinear. Hence, at small physical scales modeling by homogeneous gaussians is inadequate, although often implicitly assumed in many reconstruction algorithms. In contrast, the Poisson model and its variance stabilized Gaussian approximation seem to provide a statistically sound description of resolution at the nanoscale. Our theory is also applicable to other imaging setups, such as telescopes.

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“…It is often derived in the setting of continuous illumination, but the Poisson model can also be motivated by means of the law of small numbers, see e.g. [47].…”

Section: Statistical Modelmentioning

confidence: 99%

“…For a comprehensive discussion and more details on the modeling see e.g. [5,47]. We emphasize that the homogeneous Gaussian model is commonly used as a proxy for "microscopy with noise" and has been investigated in many studies.…”

Section: Homogeneous Gaussian Model (Hg)mentioning

confidence: 99%

What is resolution? A statistical minimax testing perspective on super-resolution microscopy

Kulaitis¹,

Munk²,

Werner³

2020

Preprint

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“…Typically, the measurements are either of random nature themselves (as e.g. in positron emission tomography (PET, see [28]), magnetic resonance imaging (MRI, see [18]) or super-resolution microscopy (see [25])) and/or additionally corrupted by measurement noise. This motivates us to consider the inverse Gaussian white noise model…”

Section: Introductionmentioning

confidence: 99%

Minimax detection of localized signals in statistical inverse problems

Pohlmann¹,

Werner²,

Munk³

2021

Preprint

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We investigate minimax testing for detecting local signals or linear combinations of such signals when only indirect data is available. Naturally, in the presence of noise, signals that are too small cannot be reliably detected. In a Gaussian white noise model, we discuss upper and lower bounds for the minimal size of the signal such that testing with small error probabilities is possible. In certain situations we are able to characterize the asymptotic minimax detection boundary. Our results are applied to inverse problems such as numerical differentiation, deconvolution and the inversion of the Radon transform.

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“…is appropriate (Munk et al, 2020). This model can also be derived from the binomial by the law of small numbers if t is large and θ is small.…”

Section: Poisson Model (P)mentioning

confidence: 99%

“…For a comprehensive discussion and more details on the modeling see e.g. (Munk et al, 2020). We emphasize that the homogeneous Gaussian model is commonly used as a proxy for "microscopy with noise" and has been investigated in many studies.…”

Section: Homogeneous Gaussian Model (Hg)mentioning

confidence: 99%

A Statistical Model of Microscope Resolution

Kulaitis¹

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I am grateful to the members of the committee for agreeing to evaluate my thesis, in particular, to Prof. Tatyana Krivobokova for taking up the duty of Korreferentin.I find myself lucky to have colleagues at the IMS. I think that the institute is a friendly, supportive and an inspiring place to work.A big thanks goes to my office mates: Florian Pein, Marco Seiler and Miguel del Álamo Ruiz for helping me with various (non)mathematical issues. Especially when I started and when I was sick. I would like to thank Natalia Khizanishvili and Heiner Keilholz for the same.My sincere gratitude goes to the RTG 2088 for organizing nice workshops, lecture series and conference funding. I would also like to thank the DFG, which partially supported my PhD through CRC 755.I would also like to acknowledge many great teachers outside of Göttingen: Virginija

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Statistical Foundations of Nanoscale Photonic Imaging

Cited by 9 publications

References 20 publications

What is resolution? A statistical minimax testing perspective on super-resolution microscopy

What is resolution? A statistical minimax testing perspective on super-resolution microscopy

Minimax detection of localized signals in statistical inverse problems

A Statistical Model of Microscope Resolution

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