2026-09-19T13:28:25Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/80737 2023-07-11 col_2142_5131 col_2142_8888 com_2142_5130 com_2142_8887 com_2142_234

Moulin, Pierre Liu, Juan 2015-09-25T20:07:55Z 2015-09-25T20:07:55Z 10000-01-01 2001 2001 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. Made available in DSpace on 2015-09-25T20:07:55Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3023125.pdf: 6835243 bytes, checksum: cd107dac0baad2a72f65eea97e304183 (MD5) Previous issue date: 2001 Embargo set by: Seth Robbins for item 82019 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 135 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001. http://hdl.handle.net/2142/80737 (MiAaPQ)AAI3023125 eng Statistics Wavelet-Based Statistical Modeling and Image Estimation text Electrical Engineering Electrical Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.