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http://dx.doi.org/10.4134/JKMS.2009.46.2.281

ORTHOGONAL MULTI-WAVELETS FROM MATRIX FACTORIZATION  

Xiao, Hongying (COLLEGE OF SCIENCE CHINA THREE GORGES UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.2, 2009 , pp. 281-294 More about this Journal
Abstract
Accuracy of the scaling function is very crucial in wavelet theory, or correspondingly, in the study of wavelet filter banks. We are mainly interested in vector-valued filter banks having matrix factorization and indicate how to choose block central symmetric matrices to construct multi-wavelets with suitable accuracy.
Keywords
multi-wavelets; PR condition; accuracy; block central symmetric matrix;
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1 C. Cabrelli, C. Heil, and U. Molter, Accuracy of lattice translates of several multidimensional refinable functions, J. Approx. Theory 95 (1998), no. 1, 5–52.   DOI   ScienceOn
2 C. Heil, G. Strang, and V. Strela, Approximation by translates of refinable functions, Numer. Math. 73 (1996), no. 1, 75–94.   DOI
3 R. Q. Jia, Approximation properties of multivariate wavelets, Math. Comp. 67 (1998), no. 222, 647–665.   DOI   ScienceOn
4 H. Xiao, Lattice structure for paraunitary linear-phase filter banks with accuracy, Acta Math. Sin. (Engl. Ser.) 22 (2006), no. 3, 679–688.   DOI
5 Q. H. Chen, C. A. Micchelli, S. Peng, and Y. Xu, Multivariate filter banks having matrix factorizations, SIAM J. Matrix Anal. Appl. 25 (2003), no. 2, 517–531.   DOI   ScienceOn
6 I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, 61. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992.
7 C. deBoor, R. A. Devore, and A. Ron, Approximation orders of FSI spaces in $L_2(R^d)$, Constr. Approx. 14 (1998), no. 4, 631–652.   DOI
8 Q. Lian, H. Xiao, and Q. Chen, Some properties on multivariate filter banks with a matrix factorization, Progr. Natur. Sci. (English Ed.) 15 (2005), no. 2, 115–125.   DOI   ScienceOn
9 G. Plonka, Approximation order provided by refinable function vectors, Constr. Approx. 13 (1997), no. 2, 221–244.   DOI
10 H. Xiao, Piecewise Linear Spectral Sequences and Wavelet Filter Banks, Doctoral Thesis, Graducate School of CAS, May 2005.