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Irregular sampling of wavelet transforms and reconstruction.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Irregular sampling of wavelet transforms and reconstruction./
Author:	Kicey, Charles John.
Description:	1 online resource (132 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 59-02, Section: B.
Contained By:	Dissertations Abstracts International59-02B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780591358896

Irregular sampling of wavelet transforms and reconstruction.
Kicey, Charles John.

Irregular sampling of wavelet transforms and reconstruction. - 1 online resource (132 pages)

Source: Dissertations Abstracts International, Volume: 59-02, Section: B.

Thesis (Ph.D.)--University of Pittsburgh, 1996.

Includes bibliographical references

We start by providing examples showing that although it is plausible that signals are characterized by their (infinite-scale) wavelet transform extrema, as conjectured by Mallat and Zhong, this is not the case even in a practical setting. Sampling wavelet transforms at extrema leads us to consider reconstruction from irregular sampling of wavelet transforms via alternating projections in Hilbert space. Here we develop some evidence indicating the importance of sampling at large values. We develop a very flexible finite-scale framework for which the reconstruction process will converge. From here, we then rigorously develop a discrete version of the algorithm and, when the wavelet generates an orthonormal multiresolution analysis, we gain a near complete understanding of the behavior of the algorithm for regular samplings. To finish, we consider band-limited wavelets, and show that under certain irregular sampling schemes we have unique reconstruction with a computable geometric rate of convergence. We improve on the original results for band-limited wavelets, gaining enough flexibility in our choice of samplings to develop a discrete version. Finally, we give an interesting application of wavelet theory that is not related to the main body of this dissertation.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9780591358896Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Irregular sampling of wavelet transforms and reconstruction.
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100 1 $a Kicey, Charles John. $3 1472823
245 1 0 $a Irregular sampling of wavelet transforms and reconstruction.
264 0 $c 1996
300 $a 1 online resource (132 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 59-02, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
502 $a Thesis (Ph.D.)--University of Pittsburgh, 1996.
504 $a Includes bibliographical references
520 $a We start by providing examples showing that although it is plausible that signals are characterized by their (infinite-scale) wavelet transform extrema, as conjectured by Mallat and Zhong, this is not the case even in a practical setting. Sampling wavelet transforms at extrema leads us to consider reconstruction from irregular sampling of wavelet transforms via alternating projections in Hilbert space. Here we develop some evidence indicating the importance of sampling at large values. We develop a very flexible finite-scale framework for which the reconstruction process will converge. From here, we then rigorously develop a discrete version of the algorithm and, when the wavelet generates an orthonormal multiresolution analysis, we gain a near complete understanding of the behavior of the algorithm for regular samplings. To finish, we consider band-limited wavelets, and show that under certain irregular sampling schemes we have unique reconstruction with a computable geometric rate of convergence. We improve on the original results for band-limited wavelets, gaining enough flexibility in our choice of samplings to develop a discrete version. Finally, we give an interesting application of wavelet theory that is not related to the main body of this dissertation.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Pittsburgh. $3 1178873
773 0 $t Dissertations Abstracts International $g 59-02B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9726876 $z click for full text (PQDT)