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In this paper, the notion of vector-valued multiresolution analysis and biorthogonal vector wavelets are introduced. The existence of biorthogonal finitely supported vector-valued wavelets associated with a pair of biorthogonal finitely supported vector-valued scaling functions is discussed. A procedure for designing a class of biorthogonal vector-valued finitely supported wavelet functions is proposed...
The notion of the higher-dimensional matrix-valued wavelet packets is proposed. A method for designing biorthogonal matrix-valued multivariate wavelet packets is developed and their properties are discussed by means of time-frequency analysis method and matrix theory. Three orthogonality formulas concerning these wavelet packets are obtained. One new Riesz basis of L2 (Rd, Cr ?? r) are constructed...
In this paper, the notion of vector-valued multiresolution analysis and biorthogonal vector-valued wavelets is introduced. The existence of compactly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. An algorithm for constructing a class of biorthogonal compactly supported vector-valued wavelet...
The concept of a generalized bivariate multiresolution structure (GBMS) of space L2(R2) is formulated. A class of multiple affine bivariate pseudoframes for subspaces of L2(R2) is introduced. The construction of a GMS of Paley-Wiener subspaces of L2(R2) is studied. The sufficient condition for the existence of pyramid decomsition scheme is presented based on such a GBMS. A class of affine bivariate...
In this paper, we introduce a sort of vector-valued wavelet packets with eight-scale dilation factor for vector-valued multivariate function space. A new procedure for designing a sort of biorthogonal vector-valued multivariate wavelet packets according to a pair of biorthogonal vector-valued scaling functions, is presented and their biorthogonality properties are characterized by virtue of matrix...
In this paper, we introduce a class of vector-valued wavelet packets of space L2(Rs, Cv), which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality properties are characterized by virtue of matrix theory, time-frequency analysis method, and operator theory...
In this paper, the notion of matrix-valued multiresolution analysis is introduced. A method for constructing biorthogonal matrix-valued wavelet packets in higher dimensions is presented and their properties are investigated by means of time-frequency analysis method, matrix theory and operator theory. Three biorthogonality formulas concerning these wavelet packets are obtained. Finally, new Riesz...
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.
In this paper, the notion of orthogonal vector-valued multivariable wavelet packets with 11-scale in higher dimensions is proposed. A novel approach for constructing them is presented. Their orthogonality property are characterized by virtue finite group theory,time-frequency analysis method and matrix theory. Orthogonality formulas are obtained.
In this paper, the concept of vector-valued multiresolution analysis is introduced and the definition of orthogonal vector-valued wavelets is given. A sufficient condition on the existence of orthogonal vector-valued wavelets is presented by virtue of matrix theory and paraunitary vector filter bank theory. A new method for constructing a class of finitely supported orthogonal vector-valued wavelets...
In this article, the notion of biorthogonal two-direction compactly supported wavelet packets with a positive integer dilation factor ?? is introduced. A new approach for constructing biorthogonal two-direction wavelet packets is developed and their properties is investigated by means of time-frequency analysis method, matrix theory and operator theory. The formulas for performing iterations and decomposition...
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