Simulated phase contrast tomography experiments using total variation regularization

Rasmus Dalgas Rasmussen

AbstractIn this thesis, phase contrast tomographic experiments are simulated in order to test and compare different variations of the reconstruction methods related to phase contrast tomography(PCT).
Computed tomography formulated as both a continuous and discrete model is presented. Different reconstruction methods, including analytical and iterative methods are also presented with some examples. This leads to a presentation of the regularization methods, where total variation (TV) regularization is the main focus for this project.
A forward model for the PCT experimental set-up called free space propagation is presented and implemented, in order to simulate experimental data. Phase retrieval techniques, which are used when reconstructing PCT data, are also presented and implemented. From these techniques a selection of complete PCT reconstruction methods are defined and put into the formulation of TV regularization. In order solve the defined TV regularization problems an optimization algorithm is implemented, which is set up to handle the PCT reconstruction methods.
Finally the optimization algorithm is used to solve different types of simulated experiments using the different methods. First the PCT methods are tested against the standard absorption based tomography method, to show some examples where PCT can be advantageous. Next the different PCT methods are tested for different scenarios and compared in order to identify the advantages and disadvantages of the different techniques.
TypeMaster's thesis [Academic thesis]
PublisherTechnical University of Denmark, Department of Applied Mathematics and Computer Science
AddressRichard Petersens Plads, Building 324, DK-2800 Kgs. Lyngby, Denmark,
SeriesDTU Compute M.Sc.-2014
NoteDTU supervisors: Per Christian Hansen,, DTU Compute, Henning Friis Poulsen, Yiqiu Dong,, DTU Compute, and Jakob Sauer Joergensen
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IMM Group(s)Scientific Computing