{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/80737"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/80737","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Wavelet-Based Statistical Modeling and Image Estimation","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. 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