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Annual Review of Statistics and Its Application
Modern statistical challenges in high-resolution fluorescence microscopy
Aspelmeier, T., Egner, A., & Munk, A.
fluorescence nanoscale microscopy, superresolution, deconvolution, nanoscopy, sparse regularization, variational multiresolution statistic, statistical imaging, sub-Poisson imaging, geometric thinning, convex optimization
Conventional light microscopes have been used for centuries for the study of small length scales down to approximately 250 nm. Images from such a microscope are typically blurred and noisy, and the measurement error in such images can often be well approximated by Gaussian or Poisson noise. In the past, this approximation has been the focus of a multitude of deconvolution techniques in imaging. However, conventional microscopes have an intrinsic physical limit of resolution. Although this limit remained unchallenged for a century, it was broken for the first time in the 1990s with the advent of modern superresolution fluorescence microscopy techniques. Since then, superresolution fluorescence microscopy has become an indispensable tool for studying the structure and dynamics of living organisms. Current experimental advances go to the physical limits of imaging, where discrete quantum effects are predominant. Consequently, this technique is inherently of a non-Gaussian statistical nature, and we argue that recent technological progress also challenges the long-standing Poisson assumption. Thus, analysis and exploitation of the discrete physical mechanisms of fluorescent molecules and light, as well as their distributions in time and space, have become necessary to achieve the highest resolution possible. This article presents an overview of some physical principles underlying modern fluorescence microscopy techniques from a statistical modeling and analysis perspective. To this end, we develop a prototypical model for fluorophore dynamics and use it to discuss statistical methods for image deconvolution and more complicated image reconstruction and enhancement techniques. Several examples are discussed in more detail, including variational multiscale methods for confocal and stimulated emission depletion (STED) microscopy, drift correction for single marker switching (SMS) microscopy, and sparse estimation and background removal for superresolution by polarization angle demodulation (SPoD). We illustrate that such methods benefit from advances in large-scale computing, for example, from recent tools from convex optimization. We argue that in the future, even higher resolutions will require more detailed models that delve into sub-Poissonian statistics.