Abstract/Details

Frame quantization theory and equiangular tight frames


2007 2007

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Abstract (summary)

In this thesis, we first consider the finite frame quantization. We make a signal-wise comparison of PCM and first order Sigma-Delta quantization. We show that Sigma-Delta quantization achieves smaller signal-wise quantization error bounds for a class of low amplitude signals. Then, we propose two new quantization methods for finite frames. First method is a variable bit-rate quantization algorithm. Given a finite signal and a predetermined error margin, this method calculates the number of bits necessary to quantize this signal within the pre-specified error margin. Second method is a 1-bit quantization technique that uses functional minimization methods. We first translate the combinatorial quantization problem into an analytic one. Then, we show that the solutions of this this analytic problem correspond to 1-bit quantized estimates of a given finite signal.

Second, we focus on finite equiangular tight frames. We show that equiangular tight frames are minimizers of certain functionals. We also give a characterization of equiangular tight frames with maximum possible redundancy.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Equiangular tight frames; Finite frames; Frame quantization
Title
Frame quantization theory and equiangular tight frames
Author
Oktay, Onur
Number of pages
142
Publication year
2007
Degree date
2007
School code
0117
Source
DAI-B 69/02, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780549453239
Advisor
Benedetto, John J.
University/institution
University of Maryland, College Park
Department
Mathematics
University location
United States -- Maryland
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3297348
ProQuest document ID
304854260
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304854260
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