Home
Resource
Various minimization problems involving the total variation in one dimension
PDF
PDF format is widely accepted and good for printing.
Plug-in required
PDF-1(575.94 kb)
Citation & Export
View Usage Statistics
Staff View

Citation & Export
Hide

Simple citation

Sznigir, Thomas. Various minimization problems involving the total variation in one dimension. Retrieved from https://doi.org/doi:10.7282/T3TX3JHB

Export

Click here for information about Citation Management Tools at Rutgers.

Statistics
Hide

Description

TitleVarious minimization problems involving the total variation in one dimension
NameSznigir, Thomas (author); Brezis, Haim (chair); Vogelius, Michael (internal member); Han, Zheng-Chao (internal member); Nguyen, Hoai-Minh (outside member); Rutgers University; School of Graduate Studies
Date Created2017
Other Date2017-10 (degree)
SubjectMathematics, Variational inequalities (Mathematics)
Extent1 online resource (iv, 132 p. : ill.)
DescriptionWe consider certain minimization problems in one dimension. The first one is the ROF filter, which was originally introduced in the context of image processing. For the one-dimensional case, we show that the problem can be reformulated as a variational inequality, and use this to extend existing regularity results. In addition, we look at the jump set of solutions and investigate its behavior as certain parameters are changed. The second functional to be considered arises in the context of regularized interpolation. The second problem is in the context of regularized interpolation, and the functional to be minimized uses the total variation as a penalty term. This problem is shown to be ill-posed with multiple solutions, and the set of solutions is described. Next, we introduce further regularization methods that lead to unique solutions, and use these regularized solutions to determine special solutions of the original problem. Finally, we consider the functional in the space L^2. To investigate it, the lower semicontinuous envelope is constructed. We then characterize the minimizers of the LSC envelope.
NotePh.D.
NoteIncludes bibliographical references
Noteby Thomas Sznigir
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3TX3JHB
Languageeng
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
Version 8.5.5
Rutgers University Libraries - Copyright ©2024