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Approximation to random process by w...

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Approximation to random process by wavelet basis.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Approximation to random process by wavelet basis./
Author:	Li, Zheng.
Description:	90 p.
Notes:	Adviser: Donald McClure.
Contained By:	Dissertation Abstracts International69-06B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3318378
ISBN:	9780549677963

Approximation to random process by wavelet basis.
Li, Zheng.

Approximation to random process by wavelet basis. - 90 p.

Adviser: Donald McClure.

Thesis (Ph.D.)--Brown University, 2008.

In this thesis we are mainly concerned about linear and nonlinear approximation to two stochastic models, which can be applied in image compression problems.

ISBN: 9780549677963Subjects--Topical Terms:

515831
Mathematics.

Approximation to random process by wavelet basis.
LDR:02308nam 2200301 a 45 001 853004
005 20100701
008 100701s2008 ||||||||||||||||| ||eng d
020 $a 9780549677963
035 $a (UMI)AAI3318378
035 $a AAI3318378
040 $a UMI $c UMI
100 1 $a Li, Zheng. $3 1019154
245 1 0 $a Approximation to random process by wavelet basis.
300 $a 90 p.
500 $a Adviser: Donald McClure.
500 $a Source: Dissertation Abstracts International, Volume: 69-06, Section: B, page: 3613.
502 $a Thesis (Ph.D.)--Brown University, 2008.
520 $a In this thesis we are mainly concerned about linear and nonlinear approximation to two stochastic models, which can be applied in image compression problems.
520 $a We shall first provide introduction to two stochastic models: Poisson model and dead leaves model. The properties and statistics about these two models will be considered in details. We shall provide an expression for the uncorrected covariance functions of models.
520 $a Our first goal is to consider the linear approximation to random processes realized from the stochastic models. We relate the asymptotic eigenvalue problem of the integral operator associated with uncorrected covariance function to the approximation error of N-term linear approximation. We learn from Karhunen-Loeve theory that optimal linear approximation error is equivalent to the tail sum of the eigenvalues. We shall consider corresponding eigenvalue problems for the 1D and 2D dead leaves model and see the conclusive result for 1D case and the inconclusive one for 2D case.
520 $a The second goal in this thesis is to consider nonlinear approximation to stochastic model by wavelet basis. We would derive an error bound for nonlinear approximation to random processes realized from 2D dead leaves model in a special case. We would see that the nonlinear approximation problem for 1D dead leaves model is very similar to that for 1D Poisson model in which Cohen and D'Ales have already proposed a nice conclusion.
590 $a School code: 0024.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 $a Brown University. $3 766761
773 0 $t Dissertation Abstracts International $g 69-06B.
790 $a 0024
790 1 0 $a McClure, Donald, $e advisor
791 $a Ph.D.
792 $a 2008
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3318378