Iterative tomographic reconstruction with priorconditioning

AbstractFor medical and research purposes the quality of tomographic reconstructions is of major importance. Priorconditioning may be a performance improving factor to iterative methods, especially for tomographic reconstruction, but has only been derived for some methods. For this purpose priorconditioned versions of the algebraic iterative methods Kaczmarz and Cimmino are derived in this paper. The priorconditioning appears in form of a priorconditioner matrix that acts as a first or second derivative operator, which causes smoothing of the solution. For this project the methods priorconditioned Kaczmarz and priorconditioned Cimmino were implemented and analyzed in Matlab. Investigations of several test problems obtained by synthetic data showed that the priorconditioned methods performed better than Kaczmarz and Cimmino if the solution was very smooth. Here we find that factors like shape and composition of the objects in the solution, amount of noise in the data and choice of the priorconditioner matrix was important for the quality of the reconstruction.
TypeBachelor thesis [Academic thesis]
PublisherTechnical University of Denmark, Department of Applied Mathematics and Computer Science
AddressRichard Petersens Plads, Building 324, DK-2800 Kgs. Lyngby, Denmark,
SeriesDTU Compute B.Sc.-2017
NoteSupervised by professor Per Christian Hansen,, DTU Compute
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IMM Group(s)Scientific Computing