Dyadic decomposition: a unified perspective on predictive, subband, and wavelet transforms

Shih-Chung Benedict Lo; Jian Hua Xuan; Huai Li; Yue Wang; Matthew T. Freedman M.D.; Seong Ki Mun

doi:10.1117/12.273906

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7 May 1997 Dyadic decomposition: a unified perspective on predictive, subband, and wavelet transforms

Shih-Chung Benedict Lo, Jian Hua Xuan, Huai Li, Yue Wang, Matthew T. Freedman M.D., Seong Ki Mun

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Proceedings Volume 3031, Medical Imaging 1997: Image Display; (1997) https://doi.org/10.1117/12.273906
Event: Medical Imaging 1997, 1997, Newport Beach, CA, United States

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.

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Shih-Chung Benedict Lo, Jian Hua Xuan, Huai Li, Yue Wang, Matthew T. Freedman M.D., and Seong Ki Mun "Dyadic decomposition: a unified perspective on predictive, subband, and wavelet transforms", Proc. SPIE 3031, Medical Imaging 1997: Image Display, (7 May 1997); https://doi.org/10.1117/12.273906

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