Files in this item
Files | Description | Format |
---|---|---|
application/pdf ![]() ![]() | (no description provided) |
Description
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 |
This item appears in the following Collection(s)
-
Dissertations and Theses - Electrical and Computer Engineering
Dissertations and Theses in Electrical and Computer Engineering -
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois