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dc.contributor.advisor Hohage, Thorsten Prof. Dr.
dc.contributor.author Maretzke, Simon
dc.date.accessioned 2019-06-12T10:54:58Z
dc.date.available 2019-06-12T10:54:58Z
dc.date.issued 2019-06-12
dc.identifier.uri http://hdl.handle.net/21.11130/00-1735-0000-0003-C12B-3
dc.language.iso eng de
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc 510 de
dc.title Inverse Problems in Propagation-based X-ray Phase Contrast Imaging and Tomography: Stability Analysis and Reconstruction Methods de
dc.type cumulativeThesis de
dc.contributor.referee Hohage, Thorsten Prof. Dr.
dc.date.examination 2019-03-04
dc.description.abstracteng Propagation-based X-ray phase contrast imaging (XPCI) and -tomography (XPCT) extend the capabilities of classical X-ray radiography and computed tomography (CT) to imaging of microscopic specimens with nanometer-sized structures, such as single biological cells. Enabled by ongoing progress in the experimental generation and control of highly coherent and intense X-ray beams, XPCI and XPCT use refraction of X-rays as a contrast-mechanism. While this enables greatly enhanced contrast compared to conventional absorption-based imaging, the inability to measure phases of the X-ray wave-field directly (the phase problem of optics) gives rise to an inverse problem: to obtain an interpretable image, the sample-induced refractive phase shifts have to be numerically reconstructed from the measured near-field intensity patterns (holograms). This thesis provides mathematical analysis of the inverse problems in XPCI and XPCT and proposes practical algorithms for their solution. Firstly, stability of image reconstruction with respect to errors in the hologram data is studied. In the linear contrast regime of weakly interacting samples, the inverse problem of XPCI is shown to be Lipschitz-stable for finitely large, i.e. compactly supported, objects and explicit bounds on the governing stability constant are derived in terms of the geometric setup parameters. The stability results are extended to several settings of interest including XPCT and, to some degree, imaging with nonlinear contrast. Moreover, it is analyzed how stability is affected by the real-world constraint that holograms are acquired by detectors of finite size. It is shown that the resulting truncation of the data gives rise to a sharp resolution limit down to which image features may be stably recovered, in agreement with the numerical aperture of the imaging system. The second, algorithmic part of this work considers regularized Newton-type methods for image reconstruction, which may flexibly exploit available a priori knowledge on the imaged object and also account for nonlinear contrast. Special emphasis is laid on making the devised algorithms computationally efficient enough for processing large-scale experimental data as encountered in XPCT at synchrotron facilities. To this end, Kaczmarz-type schemes are proposed as well as efficient formulas, termed generalized SART, for the computation of the individual Kaczmarz iterates, exploiting the specific mathematical structure of tomographic inverse problems. The capabilities of the novel reconstruction methods in terms of image-quality and computational performance are assessed for different experimental data sets. The theoretical results and numerical algorithms of this thesis may be adapted to a wide range of imaging modalities beyond XPCI and XPCT. de
dc.contributor.coReferee Salditt, Tim Prof. Dr.
dc.contributor.thirdReferee Luke, Russell Prof. Dr.
dc.contributor.thirdReferee Plonka-Hoch, Gerlind Prof. Dr.
dc.contributor.thirdReferee Ropers, Claus Prof. Dr.
dc.contributor.thirdReferee Werner, Frank Dr.
dc.subject.eng X-ray imaging de
dc.subject.eng phase contrast de
dc.subject.eng tomography de
dc.subject.eng in-line holography de
dc.subject.eng image reconstruction de
dc.subject.eng a priori constraints de
dc.subject.eng stability de
dc.subject.eng Kaczmarz-type methods de
dc.identifier.urn urn:nbn:de:gbv:7-21.11130/00-1735-0000-0003-C12B-3-7
dc.affiliation.institute Fakultät für Mathematik und Informatik de
dc.subject.gokfull Mathematics (PPN61756535X) de
dc.identifier.ppn 1667339435

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