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Title Knowledge-Based Tomography Algorithms
Author Jørgensen, Jakob Heide (Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Supervisor Hansen, Per Christian (Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Institution Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
Thesis level Master's thesis
Year 2009
Abstract In this thesis a large-scale method is developed for three-dimensional grain mapping of undeformed polycrystalline materials from diffraction data. It is shown that the reconstruction of each grain in a sample amounts to a tomography problem. A priori knowledge of the grain shape motivates the use of a Total Variation (TV) regularisation scheme, which emphasises localised, non-smooth reconstructions. An optimised gradient projection algorithm is constructed and applied to compute the TV-regularised solution, i.e., the grain map reconstruction. Relevant theory from inverse problems, optimisation and general tomography is presented, and examples of tomographic reconstruction using the filtered backprojection algorithm and iterative methods are given. The feasibilty of the developed grain mapping method is established by applying it to simulated data. It is demonstrated that the single grain reconstructions produced by the developed method are qualitatively correct and compare favourably to ART and CGLS reconstructions. This is especially the case, when only a few projections of the grain are available or for high relative noise levels. The method is shown to be efficient for large-scale problems that arise for fine discretisations of the sample. The collection of single grain reconstruction to full grain maps is described and a method for re-solving ambiguities is demonstrated.
Imprint Technical University of Denmark (DTU) : Kgs. Lyngby, Denmark
Series IMM-M.Sc.-2009-55
Fulltext
Original PDF ep09_55_net.pdf (3.35 MB)
Admin Creation date: 2009-10-13    Update date: 2010-08-25    Source: dtu    ID: 251063    Original MXD