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Title:Wavelet-Based Statistical Modeling and Image Estimation
Author(s):Liu, Juan
Doctoral Committee Chair(s):Moulin, Pierre
Department / Program:Electrical Engineering
Discipline:Electrical Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Statistics
Abstract:Third, it has been noticed in image estimation practice that a translation invariant (TI) wavelet transform enhances estimation performance. We analyze the conventional complete wavelet transform and the TI wavelet transform from the viewpoints of approximation and estimation theory. First, we show that the TI expansion produces smaller approximation error when approximating smooth functions, and mitigates Gibbs artifacts when approximating discontinuous functions. Second, we study TI estimators and show that under mild conditions, replacing an estimator with its TI version will not worsen the estimation performance as measured by the minimax or Bayes risk.
Issue Date:2001
Type:Text
Language:English
Description:135 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.
URI:http://hdl.handle.net/2142/80737
Other Identifier(s):(MiAaPQ)AAI3023125
Date Available in IDEALS:2015-09-25
Date Deposited:2001


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