Ray-Tracing Problems for Tomographic Reconstruction in Materials Science | Camilla H. Trinderup
| | Abstract | This master thesis deals with the formulation of a mathematical model for the General Ray Tracing Problem seen in the context of a di ffraction problem. The experimental set-up that lies behind the model takes basis in the science of crystallography. The model is an inverse problem and a discrete setting of it will be considered throughout the thesis. With the purpose of gaining a thorough understanding of the problem, is a simpli fied model considered at first. The analysis of this model revealed weaknesses about the model, which were factors that could then be encountered in the formulation of a more complex model. In order to make the model more complex and by this reaching a model describing the real experiment better is a blurring of the diffraction patterns is introduced. To gain an understanding of the model is the Singular Value Decomposition used as a tool for the analysis of the problem. For solving the inverse problem, di fferent classes of iterative methods are considered. As well as presenting the fi ndings of the model will the thesis present simulation studies and evaluations of the performance of the iterative solvers in accordance with these simulated test problems. | | Type | Master's thesis [Academic thesis] | | Year | 2011 | | Publisher | Technical University of Denmark, DTU Informatics, E-mail: reception@imm.dtu.dk | | Address | Asmussens Alle, Building 305, DK-2800 Kgs. Lyngby, Denmark | | Series | IMM-M.Sc.-2011-79 | | Note | | | Electronic version(s) | [pdf] | | Publication link | http://www.imm.dtu.dk/English.aspx | | BibTeX data | [bibtex] | | IMM Group(s) | Scientific Computing |
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