Mathematics – Numerical Analysis
Scientific paper
2011-11-22
Mathematics
Numerical Analysis
11 pages
Scientific paper
A multivariate biorthogonal wavelet system can be obtained from a pair of biorthogonal multivariate refinement masks in Multiresolution Analysis setup. Some multivariate refinement masks may be decomposed into lower dimensional refinement masks. Although tensor product is a popular way to construct a decomposable multivariate refinement mask from lower dimensional refinement masks, it may not be the only method that can achieve this. 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.
Hur Youngmi
Zheng Fang
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