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Proceedings Paper

Dyadic decomposition: a unified perspective on predictive, subband, and wavelet transforms
Author(s): Shih-Chung Benedict Lo; Jian Hua Xuan; Huai Li; Yue Wang; Matthew T. Freedman M.D.; Seong Ki Mun
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Paper Abstract

A decomposition method generalized from Haar transform has been derived. This general form can exactly describe dyadic doublet-type transforms such as orthogonal wavelets. Another general form based on the binomial filter can describe dyadic triplet-type transforms such as biorthogonal wavelets. Both systems can be unified by the delta function basis decomposition system. In this paper, (a) the relationship between various types of dyadic transforms are shown; (b) methods of filter design to produce low entropy are suggested; and (c) adaptive decomposition using different transformation kernels is derived through the doublet and triplet systems. The property of low entropy in the decomposed data sequence is used as a major criterion for comparing various methods. Although we provide substantial derivations regarding the predictive approaches, detailed methods are given both in theoretical development and on implementation of dyadic decomposition methods.

Paper Details

Date Published: 7 May 1997
PDF: 16 pages
Proc. SPIE 3031, Medical Imaging 1997: Image Display, (7 May 1997); doi: 10.1117/12.273906
Show Author Affiliations
Shih-Chung Benedict Lo, Georgetown Univ. Medical Ctr. (United States)
Jian Hua Xuan, Georgetown Univ. Medical Ctr. (United States)
Huai Li, Georgetown Univ. Medical Ctr. (United States)
Yue Wang, Georgetown Univ. Medical Ctr. (United States)
Matthew T. Freedman M.D., Georgetown Univ. Medical Ctr. (United States)
Seong Ki Mun, Georgetown Univ. Medical Ctr. (United States)

Published in SPIE Proceedings Vol. 3031:
Medical Imaging 1997: Image Display
Yongmin Kim, Editor(s)

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