Orthogonal Matrix-valued Wavelet Research Articles

The Research of Orthogonal Symmetric Matrix-Valued Wavelets Packets with Multiscale and Applications

Material science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this work, we introduce orthogonal matrix-valued wavelets with poly-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 matrix-valued scaling function guarantees the existence of orthogonal matrix-valued wavelet functions. Secondly, we propose a construction algorim for compactly supported orthog onal two-directional matrix-valued wavelet packets. Lastly, A method for constructing a class of compactly supported orthogonal matrix-valued wavelets is presented by means of matrix theory.

The Characteristics Concerning a Class of Orthogonal Multivariate Matrix-Valued Scaling Functions and Frame Packets

Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. In this work, the notion of matrix-valued multiresolution analysis of space is introduced. A method for constructing orthogonal matrix-valued ternary wavelet packs is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are provided. Finally, new orthonormal wavelet pack bases of space are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

On Existence of Matrix-Valued Wavelets

Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. In this paper, we investigate the existence of matrix-valued wavelet associated with a matrix-valued multireslution analysis. By using operator polar decomposition, we provide a new proof for the existence of matrix-valued wavelets. We prove that, like in the scalar case, every matrix-valued multiresolution analysis guarantees the existence of an orthogonal matrix-valued wavelet.

An Algorithm and Characteristics Concerning a Sort of Orthogonal Ternary Matrix-Valued Frame Wavelet Packs

In this work, the notion of matrix-valued multiresolution analysis of space L2(Rn, Cs×s) is introduced. A method for constructing orthogonal matrix-valued ternary wavelet packs is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are provided. Finally, new orthonormal wavelet pack bases of space L2(Rn, Cs×s) are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

The Orthogonality Character of Matrix Univariate Wavelet Packets Concerning an Integer Factor

The notion of matrix-valued multiresolution analysis. A procedure for designing orthogonal matrix-valued univariate wavelet packets is presented and their orthogonality properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Finally, one new orthonormal basis of are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

Construction and properties of orthogonal matrix-valued wavelets and wavelet packets

In this paper, we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets with arbitrary integer dilation factor m. A necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets is derived by virtue of paraunitary vector filter bank theory. An algorithm for constructing compactly supported m- scale orthogonal matrix-valued wavelets is presented. The notion of orthogonal matrix-valued wavelet packets is proposed. Their properties are investigated by means of time–frequency method, operator theory and matrix theory. In particular, it is shown how to construct various orthonormal bases of space L 2( R, C r× r ) from these wavelet packets, and the orthogonal decomposition relation is also given.

The properties of orthogonal matrix-valued wavelet packets in higher dimensions

In the paper matrix-valued multiresolution analysis and matrix-valued wavelet packets of spaceL 2(R n ,C s x s) are introduced. A procedure for constructing a class of matrix-valued wavelet packets in higher dimensions is proposed. The properties for the matrix-valued multivariate wavelet packets are investigated by using integral transform, algebra theory and operator theory. Finally, a new orthonormal basis ofL 2(R n ,C s x s) is derived from the orthogonal multivariate matrix-valued wavelet packets.