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What is resolution? A statistical minimax testing perspective on superresolution microscopy. (English) Zbl 1483.62117

The authors suggest a statistical description, which allows one to understand both the effect of the experimental setup and the random nature of photon counts on the resulting resolution. On the one hand, for Poisson measurements, they get linear dependence of the (minimax) detection boundary on the full width at half maximum (FWHM) and on the other hand, for a homogeneous Gaussian model the dependence of resolution is nonlinear. They conclude that at small physical scales modeling by homogeneous Gaussians is inadequate. In comparison to the Poisson model, that seems to provide a statistically sound description of resolution at the nanoscale. Their theory seems to be also applicable to other imaging setups.

MSC:

62H35 Image analysis in multivariate analysis
62C20 Minimax procedures in statistical decision theory
62F03 Parametric hypothesis testing
62P30 Applications of statistics in engineering and industry; control charts
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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