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dc.contributor.advisorHenson, V. Emden
dc.contributor.authorRobinson, Bruce T.
dc.date.accessioned2013-02-15T23:32:55Z
dc.date.available2013-02-15T23:32:55Z
dc.date.issued1994-06
dc.identifier.urihttp://hdl.handle.net/10945/28382
dc.description.abstractThe problem of reconstructing an image from its Radon transform profiles is outlined. This problem has medical, industrial and military applications. Using the computer assisted tomography (CAT) scan as an example, a discretization of the problem based on natural pixels is described, leading to a symmetric linear system that is in general smaller than that resulting from the conventional discretization. The linear algebraic properties of the system matrix are examined, and the convergence of the Gauss-Seidel iteration applied to the linear system is established. Next, multilevel technology is successfully incorporated through a multilevel projection method (PML) formulation of the problem. This results in a V-cycle algorithm, the convergence of which is established. Finally, the problem of spotlight computed tomography, where high quality reconstructions for only a portion of the image are required, is outlined. We establish the formalism necessary to apply fast adaptive composite (FAC) grids in this setting, and formulate the problem in a block Gauss-Seidel form. Numerical results and reconstructed images are presented which demonstrate the usefulness of these two multilevel approachesen_US
dc.description.urihttp://archive.org/details/multilevelapproa00robi
dc.format.extent174 p.;28 cm.en_US
dc.language.isoen_US
dc.publisherMonterey, California. Naval Postgraduate Schoolen_US
dc.subject.lcshApplied Mathematicsen_US
dc.titleA multilevel approach to the algebraic image reconstruction problemen_US
dc.typeThesisen_US
dc.contributor.schoolNaval Postgraduate School
dc.contributor.departmentApplied Mathematics
dc.description.serviceMajor, United States Armyen_US
etd.thesisdegree.namePh.D. in Applied Mathematicsen_US
etd.thesisdegree.levelDoctoralen_US
etd.thesisdegree.disciplineApplied Mathematicsen_US
etd.thesisdegree.grantorNaval Postgraduate Schoolen_US
dc.description.distributionstatementApproved for public release; distribution is unlimited.


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