Abstract/Details

Optimal compression and numerical stability for Gegenbauer reconstructions with applications


2009 2009

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Abstract (summary)

Reconstruction methods are characterized by their respective domain and range spaces as well as the degree to which objectives such as artifact suppression, source data compression and numerical stability are optimized. The Gegenbauer reconstruction method operates on a variety of source data spaces, mapping the domain onto a finite set of Gegenbauer polynomial basis functions. The method then expands the Gegenbauer coefficients on sub-domains of physical space segmented by presumed jump discontinuities in the source data. The absence of jump discontinuities within each sub-domain assures spectral convergence as long as reconstruction parameters lambda and m are judiciously chosen and linearly track the resolution N as it grows without bound.

The explicit benefit of Gegenbauer reconstruction to eliminate Gibbs artifacts has been understood for nearly two decades. But an accompanying implicit benefit is the ability to significantly compress source data prior to reconstruction. Unfortunately, the choice of Gegenbauer reconstruction parameters is limited by regions of numerical instability as either parameter, lambda or m, increases.

Prior studies assumed lambda and m to be linearly tied to N then characterized the bounds of instability as well as recommended safe reconstruction parameter combinations. Subsequent work demonstrated how to predict source data analyticity, of which a priori knowledge is required to minimize reconstruction error. This thesis complements such previous studies and recommends new Gegenbauer reconstruction parameter guidelines based on a suite of parameter optimizations spanning seven unique objectives. The first three of these objectives are achieved using asymptotic analysis while the remaining four are met using traditional numerical objective minimization techniques.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Fourier reconstructions; Gegenbauer reconstructions; Reconstruction
Title
Optimal compression and numerical stability for Gegenbauer reconstructions with applications
Author
Park, Russell W.
Number of pages
252
Publication year
2009
Degree date
2009
School code
0010
Source
DAI-B 70/06, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781109201468
University/institution
Arizona State University
University location
United States -- Arizona
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3361850
ProQuest document ID
304844732
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304844732
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