The characterization of vector-valued multivariate wavelet packets associated with a dilation matrix

Xiao-Feng Wang, Hongwei Gao and Feng Jinshun

Chaos, Solitons & Fractals, 2009, vol. 42, issue 4, 1959-1966

Abstract: In this work, we introduce the notion of vector-valued multiresolution analysis and vector-valued multivariate wavelet packets associated with an arbitrary integer-valued dilation matrix. A novel method for constructing higher-dimensional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas regarding the wavelet packets are provided. Orthogonality decomposition relation formulas of the space L2(Rs)r are obtained by constructing a series of subspaces of the vector-valued wavelet packets. Finally, several orthonormal wavelet packet bases of L2(Rs)r are constructed from these wavelet packets. Relation to some physical theories such as fractal theory and E-infinity theory is also discussed.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:42:y:2009:i:4:p:1959-1966

DOI: 10.1016/j.chaos.2009.03.200

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