Multiple Vector-valued Wavelet Research Articles

The Orthogonality Characters of Multiple Vector-Valued Ternary Wavelets and Applications in Theoretical Physics

Wavelet analysis has been the focus of active research for twenty years, both in theory and applications. In this work, we develop the concept of a class of multiple vector-valued trivariate wavelet wraps with a dilation matrix. A new method for constructing multiple vector-valued trivariate wavelet wraps is proposed. Their characters are investigated by means of operator technique, time-frequency analysis method and matrix theory. There orthogonality formulas regarding the wavelet wraps are provided. Orthogonality decomposition relation formulas of the space L2(R3, Cr×r)are obtained by constructing a series of subspaces of the multiple vector-valued wavelet wraps. Furthermore, several orthonormal wavelet wrap bases of space L2(R3, Cr×r) are constructed from the wavelet wraps. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. Relation to theoretical physics is also discussed.

An Algorithm for Designing a Sort of Biorthogonal Multiple Vector-valued Wavelets and their Properties

An Algorithm for Designing a Sort of Biorthogonal Multiple Vector-valued Wavelets and their Properties

Existence and characterization of orthogonal multiple vector-valued wavelets with three-scale

In this article, we introduce orthogonal multiple vector-valued wavelets with three-scale, which are wavelets for vector fields, based on the notion of full rank subdivision operators. It is demonstrated that, like in the scalar and multiwavelet case, the existence of an orthogonal multiple vector-valued scaling function guarantees the existence of orthogonal multiple vector-valued wavelet functions. In this context, however, scaling functions as well as wavelet functions turn out to be multiple vector-valued functions. A method for constructing a class of orthogonal multiple vector-valued compactly supported wavelets is presented by means of matrix theory. The properties of the multiple vector-valued wavelet packets are characterized by virtue of operator theory and time–frequency analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Relation to some physical theories such as E-infinity Cantorian spacetime theory and fractal theory is also discussed.

CHARACTERIZATIONS OF A CLASS OF ORTHOGONAL MULTIPLE VECTOR-VALUED WAVELET PACKETS

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, Cs × s) are constructed from these multiple vector-valued wavelet packets.

Design and characterizations of a class of orthogonal multiple vector-valued wavelets with 4-scale

The notion of vector-valued multiresolution analysis of space L 2 ( R , C s × s ) is introduced and the definition of orthogonal multiple vector-valued wavelets with 4-scale is given. First we obtain a necessary and sufficient condition on the existence of orthogonal multiple vector-valued wavelets by means of paraunitary vector filter bank theory. Second we propose an algorithm for constructing a class of compactly supported orthogonal multiple vector-valued wavelets. Finally, the notion of orthogonal multiple vector-valued wavelet packets is introduced. Their characterizations are presented by virtue of matrix theory, time–frequency analysis method and operator theory. In particular, orthonormal bases of space L 2 ( R , C s × s ) are constructed from these wavelet packets. Relation to some physical theories such as E-infinity theory is also discussed.

A study of biorthogonal multiple vector-valued wavelets

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.

Biorthogonal multiple vector-valued multivariate wavelet packets associated with a dilation matrix

In this paper, the notion of multiple vector-valued multiresolution analysis of space L 2 ( R s , C r × r ) is introduced. A method for constructing biorthogonal multiple vector-valued wavelet packets in higher dimensions is presented and their properties is 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 bases of space L 2( R s , C r× r ) is obtained by constructing a series of subspaces of biorthogonal multiple vector-valued wavelet packets.

Existence and construction of compactly supported biorthogonal multiple vector-valued wavelets

In this paper, we introduce biorthogonal multiple vector-valued wavelets which are wavelets for vector fields. We 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. Finally, we investigate the construction of a class of compactly supported biorthogonal multiple vector-valued wavelets.