||Knowledge-Based Tomography Algorithms
||Jørgensen, Jakob Heide (Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
||Hansen, Per Christian (Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
||Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
||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.
||Technical University of Denmark (DTU) : Kgs. Lyngby, Denmark
Creation date: 2009-10-13
Update date: 2010-08-25