@MASTERSTHESIS\{IMM2014-07012,
    author       = "R. D. Rasmussen",
    title        = "Simulated phase contrast tomography experiments using total variation regularization",
    year         = "2014",
    school       = "Technical University of Denmark, Department of Applied Mathematics and Computer Science",
    address      = "Richard Petersens Plads, Building 324, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    type         = "",
    note         = "{DTU} supervisors: Per Christian Hansen, pcha@dtu.dk, {DTU} Compute, Henning Friis Poulsen, Yiqiu Dong, yido@dtu.dk, {DTU} Compute, and Jakob Sauer Joergensen",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "In 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."
}