Coset sum: An alternative to the tensor product in wavelet construction

Youngmi Hur, Fang Zheng

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A multivariate biorthogonal wavelet system can be obtained from a pair of multivariate biorthogonal refinement masks in multiresolution analysis setup. Some multivariate refinement masks may be decomposed into lower dimensional refinement masks. Tensor product is a popular way to construct a decomposable multivariate refinement mask from lower dimensional refinement masks. We present an alternative method, which we call coset sum, for constructing multivariate refinement masks from univariate refinement masks. The coset sum shares many essential features of the tensor product that make it attractive in practice: 1) it preserves the biorthogonality of univariate refinement masks, 2) it preserves the accuracy number of the univariate refinement mask, and 3) the wavelet system associated with it has fast algorithms for computing and inverting the wavelet coefficients. The coset sum can even provide a wavelet system with faster algorithms in certain cases than the tensor product. These features of the coset sum suggest that it is worthwhile to develop and practice alternative methods to the tensor product for constructing multivariate wavelet systems. Some experimental results using 2-D images are presented to illustrate our findings.

Original languageEnglish
Article number6469231
Pages (from-to)3554-3571
Number of pages18
JournalIEEE Transactions on Information Theory
Volume59
Issue number6
DOIs
Publication statusPublished - 2013 Jun 3

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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