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@PHDTHESIS{Doberstein:793143,
author = {Doberstein, Christian},
othercontributors = {Berkels, Benjamin and Melcher, Christof},
title = {{J}oint exit wave reconstruction and multimodal
registration of transmission electron microscopy image
series},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
reportid = {RWTH-2020-06672},
pages = {1 Online-Ressource (VIII, 148 Seiten) : Illustrationen,
Diagramme},
year = {2020},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, RWTH Aachen University, 2020},
abstract = {Images generated with a transmission electron microscope
(TEM) can reveal information up to the scale of individual
atoms. However, the information contained in a TEM image is
blurred by aberrations and the partial coherence of the
electron beam. Furthermore, the images correspond to the
squared amplitude of the image plane electron wave and are
thus missing valuable information about the phase. Exit wave
reconstruction attempts to solve these problems by
reconstructing the electron wave at the exit plane of the
specimen, the so-called exit wave, from a series of images
recorded with varying focus of the objective lens. This
introduces the additional problem of aligning the image
series, which is crucial for a successful reconstruction of
the exit wave. One possible approach to reconstructing the
exit wave involves the minimization of a least squares
functional, which is implemented by the well-known MIMAP and
MAL algorithms. The MIMAP and MAL algorithms solve the
registration problem by alternatingly optimizing the exit
wave and the registration. In this thesis, a novel objective
functional $E_\sigma$ for the joint optimization of the exit
wave and the registration is proposed. The properties of the
forward model of TEM image simulation, which is given by a
weighted autocorrelation of the exit wave, are investigated
on the basis of the weighted cross-correlation and the novel
notion of $\star$-separable weights. The most important
weight functions (commonly called transmission
cross-coefficients, TCCs) for TEM image simulation are
analyzed and integrated into the present framework. The
results regarding the forward model are then used for the
analysis of the inverse problem. It is shown that the data
term of $E_\sigma$ is not coercive for $\star$-separable
TCCs, which in particular implies that the MAL functional is
not coercive. One of the main results is the existence of
minimizers of the objective functional $E_\sigma$, which is
shown with the direct method. Additionally, it is shown that
the objective functional is not convex in general. These
results are complemented by a numerical analysis, which
includes the discretization of the objective functional and
the treatment of several problems regarding the numerical
minimization of $E_\sigma$. A novel preconditioner for the
exit wave is proposed, showing a reduction of the number of
iterations for a given residual energy. The least squares
sum in the data term of the objective functional is usually
calculated by summing the squared differences of the
simulated and experimental images over the same domain for
each image. A novel method for the dynamic adjustment of
these domains based on the current estimate for the
registration is proposed, which allows to use the full image
data for the reconstruction while at the same time avoiding
the need for a continuation of the images. Numerical
experiments are presented that evaluate the utility of the
preconditioner and compare the alternating optimization
approach with the joint optimization of the exit wave and
the registration. Finally, a numerical experiment shows the
result of reconstructing the exit wave for a real image
series.},
cin = {111410 / 110000},
ddc = {510},
cid = {$I:(DE-82)111410_20170801$ / $I:(DE-82)110000_20140620$},
pnm = {GSC 111: Aachen Institute for Advanced Study in
Computational Engineering Science (AICES) (24613455)},
pid = {G:(GEPRIS)24613455},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2020-06672},
url = {https://publications.rwth-aachen.de/record/793143},
}
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