Estimating rigid motion in sparse sequential dynamic imaging: with application to nanoscale fluorescence microscopy

by Alexander Hartmann
Doctoral thesis
Date of Examination:2016-04-22
Date of issue:2017-04-05
Advisor:Prof. Dr. Axel Munk
Referee:Prof. Dr. Axel Munk
Referee:Prof. Dr. Stephan Huckemann
Persistent Address: http://dx.doi.org/10.53846/goediss-6237

 

 

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Abstract

English

In this work, we deal with sequences of pixel images (frames) which are noisy shifted, rotated, and scaled versions of some unknown image f. Moreover, those frames are sparse in the sense that they do not show the whole transformed (and noisy) image f but only relatively few pixels (at random locations). If the sequence contains enough frames, it is likely that every pixel is observed in at least one of them, and summing up all frames yields a rather complete version of the unknown image. However, since the single frames are subject to rigid motions, the result is blurred. This situation comes up in single marker switching (SMS) microscopy. In applications, the frames are often calibrated by tracking the positions of so-called fiducial markers (bright spots that are fixed to the specimen and appear in every frame). This method is technically demanding and has further drawbacks. We propose a purely statistical reconstruction method based on parametric models for the drift, rotation, and scaling functions, where we estimate those parameters by minimizing certain functionals. We prove consistency of our M-estimators, asymptotic normality of the rotation and scaling parameter estimators, and uniform tightness of the drift parameter estimator. Furthermore, we test our M-estimators in a simulation study with various parametric motion models and statistical error models. Last but not least, we apply our method to SMS microscopy data and construct bootstrap confidence bands for the drift, rotation, and scaling functions.
Keywords: motion estimation; image registration; semiparametrics; M-estimation; nanoscale fluorescence microscopy; super resolution microscopy; asymptotic normality; sparsity; registration
 
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