A study of biorthogonal multiple vector-valued wavelets

Jincang Han, Zhengxing Cheng and Qingjiang Chen

Chaos, Solitons & Fractals, 2009, vol. 40, issue 4, 1574-1587

Abstract: The notion of vector-valued multiresolution analysis is introduced and the concept of biorthogonal multiple vector-valued wavelets which are wavelets for vector fields, is introduced. It is proved that, like in the scalar and multiwavelet case, the existence of a pair of biorthogonal multiple vector-valued scaling functions guarantees the existence of a pair of biorthogonal multiple vector-valued wavelet functions. An algorithm for constructing a class of compactly supported biorthogonal multiple vector-valued wavelets is presented. Their properties are investigated by means of operator theory and algebra theory and time-frequency analysis method. Several biorthogonality formulas regarding these wavelet packets are obtained.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:40:y:2009:i:4:p:1574-1587

DOI: 10.1016/j.chaos.2007.09.037

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