Tight Frames of Compactly Supported Multivariate Multi-wavelets

Maria Charina; Charles K. Chui; Wenjie He

doi:10.1016/j.cam.2009.09.038

Tight Frames of Compactly Supported Multivariate Multi-wavelets

Maria Charina, Charles K. Chui, Wenjie He

University of Missouri-St. Louis

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Abstract

This paper is devoted to the study and construction of compactly supported tight frames of multivariate multi-wavelets. In particular, a necessary condition for their existence is derived to provide some useful guide for constructing such MRA tight frames, by reducing the factorization task of the associated polyphase matrix-valued Laurent polynomial to that of certain scalar-valued non-negative ones. We illustrate our construction method with examples of both multivariate scalar- and vector-valued subdivision schemes. Since our constructions for C1 and C2 piecewise cubic schemes are quite involved, we also include the corresponding Matlab code in the Appendix.

Original language	American English
Journal	Journal of Computational and Applied Mathematics
Volume	233
DOIs	https://doi.org/10.1016/j.cam.2009.09.038
State	Published - Feb 1 2010

Disciplines

Mathematics
Applied Mathematics
Analysis

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AB - This paper is devoted to the study and construction of compactly supported tight frames of multivariate multi-wavelets. In particular, a necessary condition for their existence is derived to provide some useful guide for constructing such MRA tight frames, by reducing the factorization task of the associated polyphase matrix-valued Laurent polynomial to that of certain scalar-valued non-negative ones. We illustrate our construction method with examples of both multivariate scalar- and vector-valued subdivision schemes. Since our constructions for C1 and C2 piecewise cubic schemes are quite involved, we also include the corresponding Matlab code in the Appendix.

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VL - 233

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ER -

Tight Frames of Compactly Supported Multivariate Multi-wavelets

Abstract

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