Narrow Results

The notion of multiple vector-valued wavelet packets is introduced. A procedure for constructing the multiple vector-valued wavelet packets is presented. Their characteristics are investigated by means of integral transformation and operator theory, and three orthogonality formulas concerning the multiple vector-valued wavelet packets. Finally, new orthogonal bases of L²(R, C^{s × s}) are constructed from these multiple vector-valued wavelet packets.

In this paper, the notion for orthogonal vector-valued multivariate wavelet packets of space L²(Rⁿ,C^s) is introduced. A method of the construction of orthogonal vector-valued wavelet packets associated with quantity dilation matrix aI (2 ≤ a ∈ Z) is presented. The properties for vector-valued multivariate wavelet packets have been investigated. Finally, a new orthogonal basis of L²(Rⁿ,C^s) is derived from the orthogonal multivariate vector-valued wavelet packets.

In the paper, the notion of univariate orthogonal waveletpackets has been generalized. First, the definition for orthogonal vector-valued wavelet packets with scale = a (2 ≤ a ∈ Z) is given. A procedure for constructing the orthogonl vector-valued wavelet packets is presented. Second, the properties of thevector-valued wavelet packets are studied. Finally, a new orthogonal basis of space L²(R ,C^s) is derived from the orthogonal vector-valued wavelet packets.

In this paper, the notion of orthogonal vector-valued wavelet packets of space L²(Rⁿ,C^s) is introduced. A procedure for constructing orthogonal vector-valued wavelet packets associated with dilation matrix 2I is presented. The properties of vector-valued wavelet packets in higher dimensions have been investigated. Finally, a new orthogonal basis of L²(Rⁿ,C^s) is obtained from the orthogonal vector-valued wavelet packets in higher dimensions.

In this paper, the notion of vector-valued wavelet packets associated with arbitrary integer-valued dilation matrix A is introduced. First, the definition for vector-valued wavelet packets is given. A method for constructing the orthogonl vector-valued wavelet packets is presented. The properties for these multivariate vector-valued wavelet packets are investigated.

In this paper, we introduce the notion of vector-valued multiresolutionanalysis and biorthogonal vector-valued wavelets. A constructive method of a class of compactly supported biorthogonal vector-valued wavelets with two-scale is proposed by using multiresolution analysis and matrix theory.