Wavelet-Based Statistical Modeling and Image Estimation

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Liu, Juan

Contributors dc:contributor

• Moulin, Pierre

• Statistics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3023125

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/80737