dc.contributor.advisor | Munk, Axel Prof. Dr. | |
dc.contributor.author | Hartmann, Alexander | |
dc.date.accessioned | 2017-04-05T09:36:10Z | |
dc.date.available | 2017-04-05T09:36:10Z | |
dc.date.issued | 2017-04-05 | |
dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-0023-3E08-0 | |
dc.identifier.uri | http://dx.doi.org/10.53846/goediss-6237 | |
dc.language.iso | eng | de |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.subject.ddc | 510 | de |
dc.title | Estimating rigid motion in sparse sequential dynamic imaging: with application to nanoscale fluorescence microscopy | de |
dc.type | doctoralThesis | de |
dc.contributor.referee | Munk, Axel Prof. Dr. | |
dc.date.examination | 2016-04-22 | |
dc.description.abstracteng | 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. | de |
dc.contributor.coReferee | Huckemann, Stephan Prof. Dr. | |
dc.subject.eng | motion estimation | de |
dc.subject.eng | image registration | de |
dc.subject.eng | semiparametrics | de |
dc.subject.eng | M-estimation | de |
dc.subject.eng | nanoscale fluorescence microscopy | de |
dc.subject.eng | super resolution microscopy | de |
dc.subject.eng | asymptotic normality | de |
dc.subject.eng | sparsity | de |
dc.subject.eng | registration | de |
dc.identifier.urn | urn:nbn:de:gbv:7-11858/00-1735-0000-0023-3E08-0-1 | |
dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
dc.subject.gokfull | Mathematics (PPN61756535X) | de |
dc.identifier.ppn | 883925036 | |