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OPTIMAL DUAL FRAMES FOR ERASURES AND DISCRETE GABOR FRAMES
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TitleOPTIMAL DUAL FRAMES FOR ERASURES AND DISCRETE GABOR FRAMES
AuthorLopez, Jerry
KeywordsFrames
Dual Frames
Vector Space
Hilbert Space
Functional Analysis
Discrete Gabor Frames
Gabor Analysis
AbstractSince their discovery in the early 1950's, frames have emerged as an important tool in areas such as signal processing, image processing, data compression and sampling theory, just to name a few. Our purpose of this dissertation is to investigate dual frames and the ability to find dual frames which are optimal when coping with the problem of erasures in data transmission. In addition, we study a special class of frames which exhibit algebraic structure, discrete Gabor frames. Much work has been done in the study of discrete Gabor frames in $\mathbb^n$, but very little is known about the $\ell^2(\mathbb)$ case or the $\ell^2(\mathbb^d)$ case. We establish some basic Gabor frame theory for $\ell^2(\mathbb)$ and then generalize to the $\ell^2(\mathbb^d)$ case.
AdviserHan, Deguang
PublisherUniversity of Central Florida
DegreePh.D.
Degree DisciplineDepartment of Mathematics
Degree GrantorSciences
Degree ProgramMathematics PhD
Graduation Date2009-01-01
TypeDoctoral dissertation
Access LevelPublic - Allow Worldwide Access
Release Date2009-05-21
RepositoryUniversity Archives
Repository CollectionElectronic Theses and Dissertations
IdentifierCFE0002614
Access Linkhttp://purl.fcla.edu/fcla/etd/CFE0002614

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