A general approach for analysis and application of discrete multiwavelet transforms

Jo Yew Tham, Lixin Shen, Seng Luan Lee, Hwee Huat Tan

Research output: Contribution to journalArticlepeer-review

121 Scopus citations

Abstract

This paper proposes a general paradigm for the analysis and application of discrete multiwavelet transforms, particularly to image compression. First, we establish the concept of an equivalent scalar (wavelet) filter bank system in which we present an equivalent and sufficient representation of a multiwavelet system of multiplicity r in terms of a set of r equivalent scalar filter banks. This relationship motivates a new measure called the good multifilter properties (GMP's), which define the desirable filter characteristics of the equivalent scalar filters. We then relate the notion of GMP's directly to the matrix filters as necessary eigenvector properties for the refinement masks of a given multiwavelet system. Second, we propose a generalized, efficient, and nonredundant framework for multiwavelet initialization by designing appropriate preanalysis and post-synthesis multirate filtering techniques. Finally, our simulations verified that both orthogonal and biorthogonal multiwavelets that possess GMP's and employ the proposed initialization technique can perform better than the popular scalar wavelets such as Daubechies'DS wavelet and the D(9/7) wavelet, and some of these multiwavelets achieved this with lower computational complexity.

Original languageEnglish (US)
Pages (from-to)457-464
Number of pages8
JournalIEEE Transactions on Signal Processing
Volume48
Issue number2
DOIs
StatePublished - 2000
Externally publishedYes

Keywords

  • Good multifilter properties
  • Image compression
  • Multiwavelets
  • Preanalysis and post-synthesis filtering
  • Wavelets

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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