Dissertation/Thesis Abstract

Optimal dual frames for erasures and discrete Gabor frames
by Lopez, Jerry, Ph.D., University of Central Florida, 2009, 132; 3357878
Abstract (Summary)

Since 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 [special characters omitted], but very little is known about the ℓ2([special characters omitted]) case or the ℓ2([special characters omitted]) case. We establish some basic Gabor frame theory for ℓ 2([special characters omitted]) and then generalize to the ℓ2([special characters omitted]) case.

Indexing (document details)
Advisor: Han, Deguang
School: University of Central Florida
School Location: United States -- Florida
Source: DAI-B 70/05, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Discrete Gabor frames, Frames, Functional analysis, Gabor analysis, Hilbert spaces, Vector spaces
Publication Number: 3357878
ISBN: 978-1-109-16142-7
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