Acceleration of Iterative Methods for Reconstruction in Tomography |
Lars Holtse Bonde
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| Abstract | In this bachelor thesis some iterative methods for solving ill-posed discrete inverse problems have been modi fied. These iterative methods are the Landweber method and the Cimmino methods. These methods produce regularized solutions that are linear combinations of some basis vectors. It has been shown that in some cases these basis vectors are a bad basis for the solution. The work in the thesis has been to introduce a preconditioner that will change these basis vectors. It has been shown that a preconditioner in some cases result in a better solution. When investigating preconditioners it was found that many natural choices were rank de ficient and therefore invalid. Therefore an a -value was inserted. The eff ect on the solution of the placement and value of the parameter was shown. Also a catalogue of proposed preconditioners and a Matlab function to produce these preconditioners has been made. The preconditioning of the two SIRT methods has been implemented in Matlab for constant relaxation parameter and a number of iterations as stopping criteria. |
| Type | Bachelor 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-B.Sc.-2011-24 |
| Note | Supervised by Professor Per Christian Hansen, pch@imm.dtu.dk, DTU Informatics |
| Electronic version(s) | [pdf] |
| Publication link | http://www.imm.dtu.dk/English.aspx |
| BibTeX data | [bibtex] |
| IMM Group(s) | Scientific Computing |