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dc.contributor.authorSlagel, Joseph Tanneren_US
dc.date.accessioned2019-06-20T08:01:49Z
dc.date.available2019-06-20T08:01:49Z
dc.date.issued2019-06-19
dc.identifier.othervt_gsexam:20485en_US
dc.identifier.urihttp://hdl.handle.net/10919/90377
dc.description.abstractNumerous scientific applications have seen the rise of massive inverse problems, where there are too much data to implement an all-at-once strategy to compute a solution. Additionally, tools for regularizing ill-posed inverse problems are infeasible when the problem is too large. This thesis focuses on the development of row-action methods, which can be used to iteratively solve inverse problems when it is not possible to access the entire data-set or forward model simultaneously. We investigate these techniques for linear inverse problems and for separable, nonlinear inverse problems where the objective function is nonlinear in one set of parameters and linear in another set of parameters. For the linear problem, we perform a convergence analysis of these methods, which shows favorable asymptotic and initial convergence properties, as well as a trade-off between convergence rate and precision of iterates that is based on the step-size. These row-action methods can be interpreted as stochastic Newton and stochastic quasi-Newton approaches on a reformulation of the least squares problem, and they can be analyzed as limited memory variants of the recursive least squares algorithm. For ill-posed problems, we introduce sampled regularization parameter selection techniques, which include sampled variants of the discrepancy principle, the unbiased predictive risk estimator, and the generalized cross-validation. We demonstrate the effectiveness of these methods using examples from super-resolution imaging, tomography reconstruction, and image classification.en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis item is protected by copyright and/or related rights. Some uses of this item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectinverse problemsen_US
dc.subjectTikhonov regularizationen_US
dc.subjectrow-action methodsen_US
dc.subjectKaczmarz methodsen_US
dc.titleRow-Action Methods for Massive Inverse Problemsen_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreeDoctor of Philosophyen_US
thesis.degree.nameDoctor of Philosophyen_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairChung, Julianneen_US
dc.contributor.committeememberChung, Matthiasen_US
dc.contributor.committeememberGugercin, Serkanen_US
dc.contributor.committeememberMarzouk, Youssefen_US
dc.contributor.committeememberTenorio, Luisen_US


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