Semiparametric Estimation of Drift, Rotation and Scaling in Sparse Sequential Dynamic Imaging: Asymptotic theory and an application in nanoscale fluorescence microscopy

Abstract

Light microscopy is an important instrument in life sciences. Over the last two decades, superresolution fluorescence microscopy techniques have been established, breaking the Abbé diffraction barrier, which before had posed a resolution limitation for over a century. The fundamentally new idea of these approaches is to use optically switchable fluorophores in order to detect features within the resolution limit imposed by the diffraction barrier consecutively instead of simultaneously. However, the relatively long imaging times needed in many modern superresolution fluorescence microscopy techniques at the nanoscale, one of them being single marker switching (SMS) microscopy, come with their own drawbacks. The challenge lies in the correct alignment of long sequences of sparse but spatially and temporally highly resolved images. This alignment is necessary due to rigid motion of the displayed object of interest or its supporting area during the observation process. In this thesis, a semiparametric model for motion correction, including drift, rotation and scaling of the imaged specimen, is used to estimate the motion and correct for it, reconstructing thereby the true underlying structure of interest. This technique is also applicable in many other scenarios, where an aggregation of a collection of sparse images is employed to obtain a good reconstruction of the underlying structure, like, for example, in real time magnetic resonance imaging (MRI).