OPTIMAL DUAL FRAMES FOR ERASURES AND DISCRETE GABOR FRAMES

Date Issued:: 2009
Abstract/Description:: 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 $\mathbb^n$, 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.

Title:	OPTIMAL DUAL FRAMES FOR ERASURES AND DISCRETE GABOR FRAMES.	23 views 10 downloads
Name(s):	Lopez, Jerry, Author Han, Deguang, Committee Chair University of Central Florida, Degree Grantor
Type of Resource:	text
Date Issued:	2009
Publisher:	University of Central Florida
Language(s):	English
Abstract/Description:	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 $\mathbb^n$, 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.
Identifier:	CFE0002614 (IID), ucf:48274 (fedora)
Note(s):	2009-05-01 Ph.D. Sciences, Department of Mathematics Doctorate This record was generated from author submitted information.
Subject(s):	Frames Dual Frames Vector Space Hilbert Space Functional Analysis Discrete Gabor Frames Gabor Analysis
Persistent Link to This Record:	http://purl.flvc.org/ucf/fd/CFE0002614
Restrictions on Access:	public
Host Institution:	UCF

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