Construction of Biorthogonal Multiwavelets Using the Lifting Scheme

Qingtang Jiang; Say Song Goh; Tao Xia

doi:10.1006/acha.2000.0318

Construction of Biorthogonal Multiwavelets Using the Lifting Scheme

Qingtang Jiang, Say Song Goh, Tao Xia

University of Missouri-St. Louis

Research output: Contribution to journal › Article › peer-review

Abstract

The lifting scheme has been found to be a flexible method for constructing scalar wavelets with desirable properties. Here it is extended to the construction of multiwavelets. It is shown that any set of compactly supported biorthogonal multiwavelets can be obtained from the Lazy matrix filters with a finite number of lifting steps. As an illustration of the general theory, compactly supported biorthogonal multiwavelets with optimum time–frequency resolution are constructed. In addition, experimental results of applying these multiwavelets to image compression are presented.

Original language	American English
Journal	Applied and Computational Harmonic Analysis
Volume	9
DOIs	https://doi.org/10.1006/acha.2000.0318
State	Published - Oct 4 2000

Disciplines

Physical Sciences and Mathematics

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abstract = " The lifting scheme has been found to be a flexible method for constructing scalar wavelets with desirable properties. Here it is extended to the construction of multiwavelets. It is shown that any set of compactly supported biorthogonal multiwavelets can be obtained from the Lazy matrix filters with a finite number of lifting steps. As an illustration of the general theory, compactly supported biorthogonal multiwavelets with optimum time–frequency resolution are constructed. In addition, experimental results of applying these multiwavelets to image compression are presented.",

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N2 - The lifting scheme has been found to be a flexible method for constructing scalar wavelets with desirable properties. Here it is extended to the construction of multiwavelets. It is shown that any set of compactly supported biorthogonal multiwavelets can be obtained from the Lazy matrix filters with a finite number of lifting steps. As an illustration of the general theory, compactly supported biorthogonal multiwavelets with optimum time–frequency resolution are constructed. In addition, experimental results of applying these multiwavelets to image compression are presented.

AB - The lifting scheme has been found to be a flexible method for constructing scalar wavelets with desirable properties. Here it is extended to the construction of multiwavelets. It is shown that any set of compactly supported biorthogonal multiwavelets can be obtained from the Lazy matrix filters with a finite number of lifting steps. As an illustration of the general theory, compactly supported biorthogonal multiwavelets with optimum time–frequency resolution are constructed. In addition, experimental results of applying these multiwavelets to image compression are presented.

UR - https://www.sciencedirect.com/science/article/pii/S106352030090318X

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Construction of Biorthogonal Multiwavelets Using the Lifting Scheme

Abstract

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