Statistical analysis methods for time varying nanoscale imaging problems
by Oskar Laitenberger
Date of Examination:2018-06-29
Date of issue:2019-03-28
Advisor:Prof. Dr. Alexander Egner
Referee:Prof. Dr. Alexander Egner
Referee:Prof. Dr. Tim Salditt
Files in this item
Name:Thesis_Veröffentlichung_20190323_schnelleWeb...pdf
Size:63.3Mb
Format:PDF
Abstract
English
Microscopy is a valuable imaging method in life sciences. It was thought for a long time that its resolution was fundamentally limited by diffraction, described by Abbe's resolution limit. But this limit only takes into account the diffraction of propagating waves. The breakthrough to high-resolution microscopy took into account the molecular properties of switchable molecules, their light and dark states. An important branch of high-resolution microscopy are stochastically switching techniques, which switch randomly selected individual molecules into the bright state while their surrounding environment remains in the dark state. Therefore they are subsumed under single molecule switching (SMS) microscopy This thesis deals with qualitative and quantitative aspects of SMS microscopy. The qualitative part deals with the drift problem of the sample during the measurement time of several minutes. Ultimately, the quality of a high resolution images suffers or is completely lost. The quantitative part deals with the development of qualitative SMS microscopy, hence the counting of molecules. Because SMS microscopy switches randomly selected molecules to the bright state and the photophysics of a molecule can be described by a time-discrete Markov chain, statistical analysis methods are excellently suited to improve both aspects. Here we present two statistical methods and demonstrate their usefulness by means of real SMS data: First, a statistical correction method for drift, which calculates a corrected image and also indicates the uncertainty of the drift estimate. Second, an extremely general counting model based on a time-discrete Markov chain which is adaptable to many dyes and proteins and does not need fluorescence standards or any a priori knowledge of transition rates . Furthermore, it is able to count high and low numbers of molecules, a challenging task not achieved so far.
Keywords: STED, STORM, PALM, GSDIM, molecule counting, image correction