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The advantages of frames and their promising fea- tures in various application have attracted a lot of int- erest and effort in recent years. In this paper, the notion of aff-ine bivariate pseudo-frames is develop-ed. The notion of a bivariate generalized multiresolution structure (BGMRS) is proposed. A novel method for constructing one BGMRS of Paley-Wiener subspaces of space is established. The...
In this paper, we introduce matrix-valued multiresolution analysis and orthogonal multiple vector-valued wavelet packets. A procedure of the construction of orthogonal multiple vector-valued wavelet packets is presented. The property of the multiple vector-valued wavelet packets has been characterized. In particular, a new orthogonal basis of L2(R,Cs??s) is drawn from these wavelet packets.
In this paper, the notion of biorthogonal vector-valued wavelet packets in higher dimensions is introduced. A feasible procedure for designing these vector-valued wavelet packets is presented. Their biorthogonality properties are characterized by using time-frequency analysis method, matrix theory and finite group theory. Three biorthogonality formulas are established.
Wavelet analysis has become a popular subject in scientific research for twenty years. In this paper, the notion of orthogonal vector-valued multivariate wavelet packets with four-scale is introduced. A method for constructing them is presented. Their orthogonal property is characterized by virtue of finite group theory, time-frequency analysis method and matrix theory. Three orthogonality formulas...
The notion of vector-valued wavelets with three-scale dilation factor associated with an orthogonal vector-valued scaling function is introduced. The existence of orthogonal vector-valued wavelets with three-scale is discussed. A necessary and sufficient condition is presented by means of the theory of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An algorithm for...
In this paper, the notion of orthogonal vector-valued wavelet packets of the space L2(Rs,Cd) is introduced. A method for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are investigated by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas with respect to the wavelet packets are established. Several...
In this paper, we show that there exist wavelet frame generated by two junctions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets. That is to say, the canonical dual wavelet frame cannot be generated by the translations and dilations of a single function.
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